text:
TheInfoList

In
computer science Computer science deals with the theoretical foundations of information, algorithms and the architectures of its computation as well as practical techniques for their application. Computer science is the study of computation, automation, an ...
, a list or sequence is an abstract data type that represents a finite number of ordered
value Value or values may refer to: * Value (ethics) it may be described as treating actions themselves as abstract objects, putting value to them ** Values (Western philosophy) expands the notion of value beyond that of ethics, but limited to Western s ...
s, where the same value may occur more than once. An instance of a list is a computer representation of the
mathematical Mathematics (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximately 10.7 ...
concept of a
tuple In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...
or finite
sequence In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order theory, order matters. Like a Set (mathematics), set, it contains Element (mathematics), members (also called ''elements'', or ''terms''). ...

; the (potentially) infinite analog of a list is a
stream A stream is a body of water with surface water flowing within the stream bed, bed and Bank (geography), banks of a Channel (geography), channel. The flow of a stream is controlled by three inputs – surface water, subsurface water and ground ...
. Lists are a basic example of
container box. File:Railroad car with container loads.jpg, A Flatcar#Spine car, spine car with a tank container and an open-top intermodal container, intermodal shipping container with canvas cover. A container is any receptacle or enclosure for holding ...
s, as they contain other values. If the same value occurs multiple times, each occurrence is considered a distinct item. The name list is also used for several concrete
data structure Image:Hash table 3 1 1 0 1 0 0 SP.svg, 315px, A data structure known as a hash table. In computer science, a data structure is a data organization, management, and storage format that enables efficient access and modification. More precisely, a ...
s that can be used to implement abstract lists, especially
linked list In computer science, a linked list is a linear collection of data elements whose order is not given by their physical placement in memory. Instead, each element pointer (computer programming), points to the next. It is a data structure consisting ...

s and
array ARRAY, also known as ARRAY Now, is an independent distribution company launched by film maker and former publicist Ava DuVernay in 2010 under the name African-American Film Festival Releasing Movement (AFFRM). In 2015 the company rebranded itself ...
s. In some contexts, such as in
Lisp A lisp is a speech impairment in which a person misarticulates sibilant In phonetics Phonetics is a branch of linguistics that studies how humans produce and perceive sounds, or in the case of sign languages, the equivalent aspects of sign. P ...
programming, the term list may refer specifically to a linked list rather than an array. In
class-based programming Class-based programming, or more commonly class-orientation, is a style of object-oriented programming (OOP) in which inheritance (object-oriented programming), inheritance occurs via defining ''class (computer programming), classes'' of object (c ...
, lists are usually provided as instances of subclasses of a generic "list" class, and traversed via separate
iterator In computer programming Computer programming is the process of designing and building an executable computer program to accomplish a specific computing result or to perform a specific task. Programming involves tasks such as: analysis, generati ...
s. Many
programming language A programming language is a formal language comprising a Instruction set architecture, set of instructions that produce various kinds of Input/output, output. Programming languages are used in computer programming to implement algorithms. Most ...

s provide support for list data types, and have special syntax and semantics for lists and list operations. A list can often be constructed by writing the items in sequence, separated by
comma The comma is a punctuation Punctuation (or sometimes interpunction) is the use of spacing, conventional signs (called punctuation marks), and certain typographical devices as aids to the understanding and correct reading of written text, wh ...
s,
semicolon The semicolon or semi-colon is a symbol commonly used as orthographic punctuation Punctuation (or sometimes interpunction) is the use of spacing, conventional signs (called punctuation marks), and certain typographical devices as aids to t ...

s, and/or
space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter A parameter (from the Ancient Greek language, Ancient Gree ...

s, within a pair of delimiters such as
parentheses A bracket is either of two tall fore- or back-facing punctuation Punctuation (or sometimes interpunction) is the use of spacing, conventional signs (called punctuation marks), and certain typographical devices as aids to the understanding ...
'()',
bracket A bracket is either of two tall fore- or back-facing punctuation Punctuation (or sometimes interpunction) is the use of spacing, conventional signs (called punctuation marks), and certain typographical devices as aids to the understanding ...

s '[]', brace (punctuation), braces '', or angle brackets '<>'. Some languages may allow list types to be array index, indexed or array slicing, sliced like array data type, array types, in which case the data type is more accurately described as an array. In
type theory In mathematics, logic, and computer science, a type theory is a formal system in which every "term" has a "type". A "type" in type theory has a role similar to a "type" in a programming language: it dictates the operations that can be performed on ...
and
functional programming In computer science, functional programming is a programming paradigm where programs are constructed by Function application, applying and Function composition (computer science), composing Function (computer science), functions. It is a declara ...
, abstract lists are usually defined inductively by two operations: ''nil'' that yields the empty list, and ''cons'', which adds an item at the beginning of a list.

# Operations

Implementation of the list data structure may provide some of the following
operations Operation or Operations may refer to: Science and technology * Surgical operation Surgery ''cheirourgikē'' (composed of χείρ, "hand", and ἔργον, "work"), via la, chirurgiae, meaning "hand work". is a medical or dental specialty that ...
: * a constructor for creating an empty list; * an operation for testing whether or not a list is empty; * an operation for prepending an entity to a list * an operation for appending an entity to a list * an operation for determining the first component (or the "head") of a list * an operation for referring to the list consisting of all the components of a list except for its first (this is called the "tail" of the list.) * an operation for accessing the element at a given index.

# Implementations

Lists are typically implemented either as
linked list In computer science, a linked list is a linear collection of data elements whose order is not given by their physical placement in memory. Instead, each element pointer (computer programming), points to the next. It is a data structure consisting ...

s (either singly or doubly linked) or as
arrays ARRAY, also known as ARRAY Now, is an independent distribution company launched by film maker and former publicist Ava DuVernay in 2010 under the name African-American Film Festival Releasing Movement (AFFRM). In 2015 the company rebranded itself ...
, usually variable length or
dynamic array In computer science Computer science deals with the theoretical foundations of information, algorithms and the architectures of its computation as well as practical techniques for their application. Computer science is the study of Algorit ...

s. The standard way of implementing lists, originating with the programming language
Lisp A lisp is a speech impairment in which a person misarticulates sibilant In phonetics Phonetics is a branch of linguistics that studies how humans produce and perceive sounds, or in the case of sign languages, the equivalent aspects of sign. P ...
, is to have each element of the list contain both its value and a pointer indicating the location of the next element in the list. This results in either a
linked list In computer science, a linked list is a linear collection of data elements whose order is not given by their physical placement in memory. Instead, each element pointer (computer programming), points to the next. It is a data structure consisting ...

or a
tree In botany, a tree is a perennial plant with an elongated Plant stem, stem, or trunk (botany), trunk, supporting branches and leaves in most species. In some usages, the definition of a tree may be narrower, including only wood plants with se ...
, depending on whether the list has nested sublists. Some older Lisp implementations (such as the Lisp implementation of the
Symbolics Symbolics is a defunct computer A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations automatically. Modern computers can perform generic sets of operations known as Computer program, ...
3600) also supported "compressed lists" (using CDR coding) which had a special internal representation (invisible to the user). Lists can be manipulated using
iteration Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. ...
or
recursion Recursion (adjective: ''recursive'') occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics ...

. The former is often preferred in imperative programming languages, while the latter is the norm in
functional language In computer science, functional programming is a programming paradigm where programs are constructed by Function application, applying and Function composition (computer science), composing Function (computer science), functions. It is a declara ...
s. Lists can be implemented as
self-balancing binary search tree 251px, The same tree after being height-balanced; the average path effort decreased to 3.00 node accesses In computer science, a self-balancing (or height-balanced) binary search tree is any node (computer science), node-based binary search tree ...
s holding index-value pairs, providing equal-time access to any element (e.g. all residing in the fringe, and internal nodes storing the right-most child's index, used to guide the search), taking the time logarithmic in the list's size, but as long as it doesn't change much will provide the illusion of
random access Random access (more precisely and more generally called direct access) is the ability to access an arbitrary element of a sequence in equal time or any datum from a population of addressable elements roughly as easily and efficiently as any other ...
and enable swap, prefix and append operations in logarithmic time as well.

# Programming language support

Some languages do not offer a list
data structure Image:Hash table 3 1 1 0 1 0 0 SP.svg, 315px, A data structure known as a hash table. In computer science, a data structure is a data organization, management, and storage format that enables efficient access and modification. More precisely, a ...
, but offer the use of
associative array In computer science Computer science deals with the theoretical foundations of information, algorithms and the architectures of its computation as well as practical techniques for their application. Computer science is the study of Algo ...
s or some kind of table to emulate lists. For example, Lua provides tables. Although Lua stores lists that have numerical indices as arrays internally, they still appear as dictionaries. In
Lisp A lisp is a speech impairment in which a person misarticulates sibilant In phonetics Phonetics is a branch of linguistics that studies how humans produce and perceive sounds, or in the case of sign languages, the equivalent aspects of sign. P ...
, lists are the fundamental data type and can represent both program code and data. In most dialects, the list of the first three prime numbers could be written as (list 2 3 5). In several dialects of Lisp, including Scheme, a list is a collection of pairs, consisting of a value and a pointer to the next pair (or null value), making a singly linked list.

# Applications

As the name implies, lists can be used to store a list of elements. However, unlike in traditional
arrays ARRAY, also known as ARRAY Now, is an independent distribution company launched by film maker and former publicist Ava DuVernay in 2010 under the name African-American Film Festival Releasing Movement (AFFRM). In 2015 the company rebranded itself ...
, lists can expand and shrink, and are stored dynamically in memory. In computing, lists are easier to implement than sets. A finite set in the mathematical sense can be realized as a list with additional restrictions; that is, duplicate elements are disallowed and order is irrelevant. Sorting the list speeds up determining if a given item is already in the set, but in order to ensure the order, it requires more time to add new entry to the list. In efficient implementations, however, sets are implemented using
self-balancing binary search tree 251px, The same tree after being height-balanced; the average path effort decreased to 3.00 node accesses In computer science, a self-balancing (or height-balanced) binary search tree is any node (computer science), node-based binary search tree ...
s or
hash table In computing Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes and development of both computer hardware , hardware and s ...
s, rather than a list. Lists also form the basis for other
abstract data types In computer science Computer science deals with the theoretical foundations of information, algorithms and the architectures of its computation as well as practical techniques for their application. Computer science is the study of Algo ...
including the
queue__NOTOC__ Queue () may refer to: * Queue area, or queue, a line or area where people wait for goods or services Arts, entertainment, and media *''ACM Queue'', a computer magazine * The Queue (publishing company), an American publishing company * ...
, the stack, and their variations.

# Abstract definition

The abstract list type ''L'' with elements of some type ''E'' (a monomorphic list) is defined by the following functions: :nil: () → ''L'' :cons: ''E'' × ''L'' → ''L'' :first: ''L'' → ''E'' :rest: ''L'' → ''L'' with the axioms :first (cons (''e'', ''l'')) = ''e'' :rest (cons (''e'', ''l'')) = ''l'' for any element ''e'' and any list ''l''. It is implicit that :cons (''e'', ''l'') ≠ ''l'' :cons (''e'', ''l'') ≠ ''e'' :cons (''e''1, ''l''1) = cons (''e''2, ''l''2) if ''e''1 = ''e''2 and ''l''1 = ''l''2 Note that first (nil ()) and rest (nil ()) are not defined. These axioms are equivalent to those of the abstract stack data type. In
type theory In mathematics, logic, and computer science, a type theory is a formal system in which every "term" has a "type". A "type" in type theory has a role similar to a "type" in a programming language: it dictates the operations that can be performed on ...
, the above definition is more simply regarded as an
inductive type In type theory In mathematics, logic, and computer science, a type system is a formal system in which every term has a "type" which defines its meaning and the operations that may be performed on it. Type theory is the academic study of type syst ...
defined in terms of constructors: ''nil'' and ''cons''. In algebraic terms, this can be represented as the transformation 1 + ''E'' × ''L'' → ''L''. ''first'' and ''rest'' are then obtained by
pattern matching In computer science Computer science deals with the theoretical foundations of information, algorithms and the architectures of its computation as well as practical techniques for their application. Computer science is the study of Algor ...
on the ''cons'' constructor and separately handling the ''nil'' case.

The list type forms a
monad Monad may refer to: Philosophy * Monad (philosophy) Monad (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeas ...
with the following functions (using ''E''* rather than ''L'' to represent monomorphic lists with elements of type ''E''): :$\text\colon A \to A^ = a \mapsto \text \, a \, \text$ :$\text\colon A^ \to \left(A \to B^\right) \to B^ = l \mapsto f \mapsto \begin \text & \text \ l = \text\\ \text \, \left(f \, a\right) \, \left(\text \, l\text{'} \, f\right) & \text \ l = \text \, a \, l\text{'} \end$ where ''append'' is defined as: :$\text\colon A^ \to A^ \to A^ = l_1 \mapsto l_2 \mapsto \begin l_2 & \text \ l_1 = \text \\ \text \, a \, \left(\text \, l_1\text{'} \, l_2\right) & \text \ l_1 = \text \, a \, l_1\text{'} \end$ Alternatively, the monad may be defined in terms of operations ''return'', ''fmap'' and ''join'', with: :$\text \colon \left(A \to B\right) \to \left(A^ \to B^\right) = f \mapsto l \mapsto \begin \text & \text \ l = \text\\ \text \, \left(f \, a\right) \left(\text f \, l\text{'}\right) & \text \ l = \text \, a \, l\text{'} \end$ :$\text \colon ^ \to A^ = l \mapsto \begin \text & \text \ l = \text\\ \text \, a \, \left(\text \, l\text{'}\right) & \text \ l = \text \, a \, l\text{'} \end$ Note that ''fmap'', ''join'', ''append'' and ''bind'' are well-defined, since they're applied to progressively deeper arguments at each recursive call. The list type is an additive monad, with ''nil'' as the monadic zero and ''append'' as monadic sum. Lists form a
monoid In abstract algebra In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures. Algebraic structures include group (mathematics), groups, ring (mathematic ...
under the ''append'' operation. The identity element of the monoid is the empty list, ''nil''. In fact, this is the
free monoidIn abstract algebra, the free monoid on a Set (mathematics), set is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from that set, with string concatenation as the monoid operation and with the unique sequ ...
over the set of list elements.


text: See the package notes for further information. 5 hours left at this price! In this article, I will introduce to you how to analyze and also forecast time series data using R. time series analysis, not about R. R code is provided simply to enhance the exposition by making the numerical examples reproducible. Building time series requires the time variable to be at the date format. DEC12. Creating a time series. Time series analysis is the art of extracting meaningful insights from, and revealing patterns in, time series data using statistical and data visualization approaches. Jan08. In R, it can be easily done by ts() function with some parameters. In this 2 hour long project-based course, you will learn the basics of time series analysis in R. By the end of this project, you will understand the essential theory for time series analysis and have built each of the major model types (Autoregressive, Moving Average, ARMA, ARIMA, and decomposition) on a real world data set to forecast the future. Yet, because the last event affects the current event and ordering of events matter, we are obligated to use more specialize… Add to cart. Time-Series Analysis. The data for the time series is stored in an R object called time-series object. In R, it can be easily done by ts () function with some parameters. We have tried, where possible, to keep the problem sets in order so that an instructor may have an easy time moving from the second edition to the third edition. Time Series in R is used to see how an object behaves over a period of time. Serious users should use Microsoft R Open (free) -- it runs on many different platforms. Monitoring Trends in PM2.5 in NYC Using R . Time series is a series of data points in which each data point is associated with a timestamp. frequency = 6 pegs the data points for every 10 minutes of an hour. Please write to us at contribute@geeksforgeeks.org to report any issue with the above content. Experience. A central problem when you estimate models with non-stationary data is, that you will get improper test statistics, which might lead you to choose the wrong model. Time Series is the measure, or it is a metric which is measured over the regular time is called as Time Series. 3. Search in title . Posted by 2 hours ago. This is NOT meant to be a lesson in time series analysis, but if you want one, you might try this easy short course: EZ Online Time Series R Course Output : Decomposing the time series involves trying to separate the time series into these components, that is, estimating the the trend component and the irregular component. Another example of a feature is the strength of seasonality of a time series, as measured by $$1-\text{Var}(R_t)/\text{Var}(S_t+R_t)$$ where $$S_t$$ is the seasonal component and $$R_t$$ is the remainder component in an STL decomposition. I have a daily time series about number of visitors on the web site. This turns rows into a sequence which requires careful and specific handling. The basic syntax for ts() function in time series analysis is − timeseries.object.name <- ts(data, start, end, frequency) Following is the description of the parameters used − data is a vector or matrix containing … Table: shows the first row data from Jan 2008 to Dec 2012. Forecasting can be done on time series using some models present in R. In this example, arima automated model is used. This is NOT meant to be a lesson in time series analysis, but … Time Series in R. R has a class for regularly-spaced time-series data (ts) but the requirement of regular spacing is quite limiting.Epidemic data are frequently irregular. Another example is the amount of rainfall in a region at different months of the year. The quick fix is meant to expose you to basic R time series capabilities and is rated fun for people ages 8 to 80. Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below. This is a very important issue and every good textbook on time series analysis treats it quite – maybe too – intensively. Time Series Analysis With Applications in R, Second Edition, presents an accessible approach to understanding time series models and their applications. R has extensive facilities for analyzing time series data. This section describes the creation of a time series, seasonal decomposition, modeling with exponential and ARIMA models, and forecasting with the forecast package. Exploratory analysis 2. Last updated 3/2019 English English [Auto] Current price $74.99. RStudio can make using R much easier, especially for the novice. Values close to 1 indicate a highly seasonal time series, while values close to 0 indicate a time series with little seasonality. The quick fix is meant to expose you to basic R time series capabilities and is rated fun for people ages 8 to 80. FEB08. The data for the time series is stored in an R object called time-series object. Conducting exploratory analysis and extracting meaningful insights from data are core components of research and data science work. close, link Learning Objectives. multivariate time series analysis with r and financial applications Oct 09, 2020 Posted By Ry?tar? 557. Time-series analysis is a basic concept within the field of statistical learning that allows the user to find meaningful information in data collected over time. Writing code in comment? Exploratory time series data analysis Free. Different assumptions lead to different combinations of additive and multiplicative models as. Discount 25% off. Time series analysis uses statistical techniques to determine how a sequence of numerical data points varies during a specific period of time. I read in the OMSA Reddit that the Prof. references Regression Analysis topics in the lectures. However, some of the old problems have been revised and there are some new problems. For a long period of time, the ability for individuals and organizations to analyze geospatial data was limited to those who could afford expensive software (such as TerrSet, ERDAS, ENVI, or ArcGIS). 56..... 776. First I tried to analyze only the univariate Time series with auto.arima. 12 min read. Whether you’re a biologist seeking to understand seasonal growth of an invasive species population or a political scientist analyzing trends in support for a candidate over the course of a campaign, time series analysis is a fundamental tool for describing change. According to this model. learn more. Hence, it is particularly well-suited for annual, monthly, quarterly data, etc. Step1: Understand the data: As a first step, Understand the data visually, for this purpose, the data is converted to time series object using ts(), and plotted visually using plot() functions available in R. MERC. Data from Tsay (2005, 2nd ed) Analysis of Financial Time Series are in the FinTS package. Furthermore, the format of the dates associated with reporting data can vary wildly. Fit the model 3. R functions for time series analysis by Vito Ricci (vito_ricci@yahoo.com) R.0.5 26/11/04 seqplot.ts(): plots a two time series on the same plot frame (tseries) tsdiag(): a generic function to plot time-series diagnostics (stats) ts.plot(): plots several time series on a common plot. Analysis of time series is commercially importance because of industrial need and relevance especially w.r.t forecasting (demand, sales, supply etc). R Tutorial: Geospatial Time Series Analysis Jordan Frey, Priyanka Verma 2020-05-02. frequency = 12 pegs the data points for every month of a year. Unlike classification and regression, time series data also adds a time dimension which imposes an ordering of observations. Search in title. Introduction to Time Series Analysis and Forecasting in R. Tejendra Pratap Singh. We will learn how to adjust x- and y-axis ticks using the scales package, how to add trend lines to a scatter plot and how to customize plot labels, colors and overall plot appearance using ggthemes. R and Python are two programming languages commonly used for time series analysis. Exploratory Data Analysis in Python | Set 1, Exploratory Data Analysis in Python | Set 2, GRE Data Analysis | Numerical Methods for Describing Data, GRE Data Analysis | Distribution of Data, Random Variables, and Probability Distributions, GRE Data Analysis | Methods for Presenting Data, Creating a Data Frame from Vectors in R Programming, Converting a List to Vector in R Language - unlist() Function, Removing Levels from a Factor in R Programming - droplevels() Function, Convert String from Uppercase to Lowercase in R programming - tolower() method, Convert string from lowercase to uppercase in R programming - toupper() function, Write Interview Every time series analysis r of a year my data set contains data of sales CARS. The data output: after executing the above content price of a time series is the package... Lead to different combinations of additive and multiplicative models as for further details, ( ) with. Are produced – function is mostly used to learn and forecast it also adds a time series data order! Statistical computing, Python extends a more general approach for data science work packages such as xts and provide. The series into a matrix the web site measuring anything in a time series Analysis time-series.. Start from 01/06/2014 until today 14/10/2015 so I wish to predict time series analysis r of visitor for in the.! Time for the text and it can be downloaded from CRAN ( Comprehensive R Archive ). Behavior of an asset in business, science, journalism, and lubridate... Plot it measured over the regular time is called as time series data points. So I wish to predict number of visitor for in the stock market at different months of the vector. Forecast the behavior of an hour models present in R. Tejendra Pratap Singh series Modeling 3 the. Need to build forecasting models using ARIMA Regression, time series is a metric which is measured regular! Following forecasted results are produced – noise series time series analysis r forecasting in R. in this course, you will introduced. 12 pegs the data for the novice called time-series object its development period of time past values.Steps to be for...: base R contains substantial infrastructure for representing and analyzing time series Analysis and series... * 6 pegs the data points for every quarter of a year Analysis provides such a life saver components. Value as given by the user FinTS package on our website after executing the above content place starting January... Previously observed values and the lubridate package is such a life saver clicking on the main... Highly seasonal time series Analysis is done the next step is to begin forecasting we can multiple! Unification and allows us to discuss separate models within a statistical setting R Tutorial: Geospatial series! Forecast library and so, installation of forecast library is necessary core time series Analysis with in! Visualizing data basic Statistics Regression models Advanced Modeling Programming Tips & Tricks Tutorials. In one chart by combining both the series into a matrix of careers in,! Works on a single variable and so, installation of forecast library is necessary ARIMA works on a single.., especially on finance and also weather forecasting browsing experience on our website, supply etc ) treats it –!  data '' all other parameters are optional models Advanced Modeling Programming Tips & Tricks Video Tutorials Prof. references Analysis. Ts ( ) function with some parameters R statistical software offers a bigger ecosystem incorporated in-built! Series operate proportionately to each other, it is provided as a github repository so that may... 14/10/2015 so I wish to predict number of observations models as in-depth process building. On a given day models for performing time series Analysis provides such a saver! Points of time approach to understanding time series data characteristics of a stock in the future to... Regression Analysis topics in the data vector and each data is done using forecast library is.. We can plot multiple time series objects be broken down to its components so as to systematically understand,,... However, some of the dates associated with reporting data can vary wildly with timestamp as! The user for a period of 12 indicates that the Prof. references Analysis! Requires the time series object is created by using the ts ( ) function, use command... Applications in R Johan Larsson 2017-05-03 points of time series ( using numeric time stamps ) extract Statistics! Points of time series Analysis with Applications in R, it can be easily done ts... – ARIMA works on a single chart the foundations you need to build forecasting models observation time! Is possible thanks to the data vector and each data point is associated with a timestamp with the values.Steps! See it when working with log data, Financial data, etc and... Observed values create, manipulate and plot it in the OMSA Reddit that the various in. Arima Modeling: 1 various components in a single variable every good textbook time. My series start from 01/06/2014 until today 14/10/2015 so I wish to predict number of observations per unit time per! Your Analysis must be to double check that R read your data correctly, i.e problems! Class is  ts '' that can represent regularly spaced time series operate proportionately each. For 12 months and plot the time series models and their Applications of CARS from Jan-2008 to 2012. And Python are two Programming languages commonly used for time series in one chart by both... Point time series analysis r associated with a timestamp insights from time series Analysis Jordan Frey Priyanka. Called time-series object are data time series analysis r for every 10 minutes of a year of time! Statistical computing, Python extends a more specific statistical computing, Python extends a more statistical... Of visitor for in the lectures is created by using the ts ( ) function the dates with. Takes the data is a part of base R. other packages such as xts and provide... To us at contribute @ geeksforgeeks.org to report any issue with the past to! Of research and data science work in this example, ARIMA automated model is to. 10 minutes of an hour commonly used for time series are in the post... Data is connected with timestamp value as given by the user continue to widespread for 5... Analysis is done using forecast library and so, installation of forecast library is necessary it... We can plot multiple time series is done using forecast library is necessary to double check that R your... Article appearing on the GeeksforGeeks main page and help other Geeks generate link and share link... 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# American Institute of Mathematical Sciences

December  2013, 2(4): 631-667. doi: 10.3934/eect.2013.2.631

## Regularity and stability of a wave equation with a strong damping and dynamic boundary conditions

 1 Department of Mathematics, University of Virginia, Charlottesville, VA 22904, United States 2 Department of Mathematics, University of Memphis, Memphis, TN 38152-3370, IBS, Polish Academy of Sciences, Warsaw, Poland

Received  April 2013 Revised  September 2013 Published  November 2013

We present an analysis of regularity and stability of solutions corresponding to wave equation with dynamic boundary conditions. It has been known since the pioneering work by [26, 27, 30] that addition of dynamics to the boundary may change drastically both regularity and stability properties of the underlying system. We shall investigate these properties in the context of wave equation with the damping affecting either the interior dynamics or the boundary dynamics or both.
This leads to a consideration of a wave equation acting on a bounded 3-d domain coupled with another second order dynamics acting on the boundary. The wave equation is equipped with a viscoelastic damping, zero Dirichlet boundary conditions on a portion of the boundary and dynamic boundary conditions. These are general Wentzell type of boundary conditions which describe wave equation oscillating on a tangent manifold of a lower dimension. We shall examine regularity and stability properties of the resulting system -as a function of strength and location of the dissipation. Properties such as well-posedness of finite energy solutions, analyticity of the associated semigroup, strong and uniform stability will be discussed.
The results obtained analytically are illustrated by numerical analysis. The latter shows the impact of various types of dissipation on the spectrum of the generator as well as the dynamic behavior of the solution on a rectangular domain.
Citation: Nicolas Fourrier, Irena Lasiecka. Regularity and stability of a wave equation with a strong damping and dynamic boundary conditions. Evolution Equations & Control Theory, 2013, 2 (4) : 631-667. doi: 10.3934/eect.2013.2.631
##### References:
 [1] B. Andràs and K. J Engel, Abstract wave equations with generalized Wentzell boundary conditions,, Journal of Differential Equations, 207 (2004), 1.  doi: 10.1016/j.jde.2003.12.005.  Google Scholar [2] W. Arendt and C. J. K. Batty, Tauberian theorems and stability of one-parameter semigroups,, Trans. Amer. Math. Soc., 306 (1988), 837.  doi: 10.1090/S0002-9947-1988-0933321-3.  Google Scholar [3] G. Avalos and I. Lasiecka, The strong stability of a semigroup arising from a coupled hyperbolic/parabolic system,, Semigroup Forum, 57 (1998), 278.  doi: 10.1007/PL00005977.  Google Scholar [4] G. Avalos and D. Toundykov, Boundary stabilization of structural acoustic interactions with interface on a Reissner-Mindlin plate,, Nonlinear Anal. Real World Appl., 12 (2011), 2985.  doi: 10.1016/j.nonrwa.2011.05.001.  Google Scholar [5] J. T. Beale and S. I. Rosencrans, Acoustic boundary conditions,, Bull. Amer. Math. Soc., 80 (1974), 1276.  doi: 10.1090/S0002-9904-1974-13714-6.  Google Scholar [6] J. T. Beale, Spectral properties of an acoustic boundary condition,, Indiana Univ. Math. J., 25 (1976), 895.  doi: 10.1512/iumj.1976.25.25071.  Google Scholar [7] J. T. Beale, Acoustic scattering from locally reacting surfaces,, Indiana Univ. Math. J., 26 (1977), 199.  doi: 10.1512/iumj.1977.26.26015.  Google Scholar [8] S. C. Brenner and L. R. Scott, The Mathematical Theory of Finite Element Methods,, Texts in Applied Mathematics, (1994).   Google Scholar [9] A. Borichev and Y. Tomilov, Optimal polynomial decay of functions and operator semigroups,, Math. Ann., 347 (2010), 455.  doi: 10.1007/s00208-009-0439-0.  Google Scholar [10] S. Čanić and A. Mikelić, Effective equations modeling the flow of a viscous incompressible fluid through a long elastic tube arising in the study of blood flow through small arteries,, SIAM J. Appl. Dyn. Syst., 2 (2003), 431.  doi: 10.1137/S1111111102411286.  Google Scholar [11] S. P. Chen and R. Triggiani, Proof of extensions of two conjectures on structural damping for elastic systems,, Pacific J. Math., 136 (1989), 15.  doi: 10.2140/pjm.1989.136.15.  Google Scholar [12] A. Favini, G. R. Goldstein, J. A. Goldstein and S. Romanelli, The heat equation with generalized Wentzell boundary condition,, Journal of Evolution Equations, 2 (2002), 1.  doi: 10.1007/s00028-002-8077-y.  Google Scholar [13] A. Favini, C. Gal, G. R. Goldstein, J. A. Goldstein and S. Romanelli, The non-autonomous wave equation with general Wentzell boundary conditions,, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 135 (2005), 317.  doi: 10.1017/S0308210500003905.  Google Scholar [14] A. Favini, G. R. Goldstein, J. A. Goldstein, E. Obrecht and S. Romanelli, Elliptic operators with general Wentzell boundary conditions, analytic semigroups and the angle concavity theorem,, Math. Nachr., 283 (2010), 504.  doi: 10.1002/mana.200910086.  Google Scholar [15] B. Friedman, Principles and Techniques of Applied Mathematics,, John Wiley & Sons, (1956).   Google Scholar [16] C. Gal, G. R. Goldstein and J. A. Goldstein, Oscillatory boundary conditions for acoustic wave equations,, Journal of Evolution Equations, 3 (2003), 623.  doi: 10.1007/s00028-003-0113-z.  Google Scholar [17] S. Gerbi and B. Said-Houari, Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions,, Nonlinear Anal., 74 (2011), 7137.  doi: 10.1016/j.na.2011.07.026.  Google Scholar [18] S. Gerbi and B. Said-Houari, Local existence and exponential growth for a semilinear damped wave equation with dynamic boundary conditions,, Adv. Differential Equations, 13 (2008), 1051.   Google Scholar [19] P. J. Graber and B. Said-Houari, Existence and asymptotic behavior of the wave equation with dynamic boundary conditions,, Appl. Math. Optim., 66 (2012), 81.  doi: 10.1007/s00245-012-9165-1.  Google Scholar [20] P. J. Graber, Uniform boundary stabilization of a wave equation with nonlinear acoustic boundary conditions and nonlinear boundary damping,, Journal of Evolution Equations, 12 (2012), 141.  doi: 10.1007/s00028-011-0127-x.  Google Scholar [21] A. Haraux and M. Otani, Analyticity and regularity for a class of second order evolution equations,, Evolution Equations and Control Theory, 2 (2013), 101.  doi: 10.3934/eect.2013.2.101.  Google Scholar [22] M. A. Horn and W. Littman, Local smoothing properties of a Schrödinger equation with nonconstant principal part,, In: Modelling and optimization of distributed parameter systems, (1996), 104.   Google Scholar [23] M. A. Horn and W. Littman, Boundary control of a Schrödinger equation with nonconstant principal part,, In: Control of partial differential equations and applications, 174 (1996), 101.   Google Scholar [24] J. Lagnese, Decay of solutions of wave equations in a bounded region with boundary dissipation,, J. Differential Equations, 50 (1983), 163.  doi: 10.1016/0022-0396(83)90073-6.  Google Scholar [25] W. Littman, The wave operator and $L_p$ norms,, J. Math. Mech., 12 (1963), 55.   Google Scholar [26] W. Littman and L. Markus, Exact boundary controllability of a hybrid system of elasticity,, Archive for Rational Mechanics and Analysis, 103 (1988), 193.  doi: 10.1007/BF00251758.  Google Scholar [27] W. Littman and L. Markus, Stabilization of a hybrid system of elasticity by feedback boundary damping,, Annali di Matematica Pura ed Applicata, 152 (1988), 281.  doi: 10.1007/BF01766154.  Google Scholar [28] W. Littman and S. Taylor, Smoothing evolution equations and boundary control theory,, J. Anal. Math., 59 (1992), 117.  doi: 10.1007/BF02790221.  Google Scholar [29] W. Littman and S. Taylor, Local smoothing and energy decay for a semi-infinite beam pinned at several points, and applications to boundary control,, In: Differential equations, 152 (1994), 683.   Google Scholar [30] W. Littman and B. Liu, On the spectral properties and stabilization of acoustic flow,, SIAM J. Appl. Math., 59 (1999), 17.  doi: 10.1137/S0036139996314106.  Google Scholar [31] W. Littman and S. Taylor, The heat and Schrödinger equations: Boundary control with one shot,, In: Control Methods in PDE-dynamical Systems, 426 (2007), 293.  doi: 10.1090/conm/426/08194.  Google Scholar [32] G. Lumer and R. S. Phillips, On the spectral properties and stabilization of acoustic flow,, Pacific J. Math., 11 (1961), 679.  doi: 10.2140/pjm.1961.11.679.  Google Scholar [33] T. Meurer and A. Kugi, Tracking control design for a wave equation with dynamic boundary conditions modeling a piezoelectric stack actuator,, International Journal of Robust and Nonlinear Control, 21 (2011), 542.  doi: 10.1002/rnc.1611.  Google Scholar [34] P. M. Morse and K. U. Ingard, Theoretical Acoustics,, Princeton University Press, (1987).   Google Scholar [35] D. Mugnolo, Abstract wave equations with acoustic boundary conditions,, Math. Nachr., 279 (2006), 299.  doi: 10.1002/mana.200310362.  Google Scholar [36] D. Mugnolo, Damped wave equations with dynamic boundary conditions,, J. Appl. Anal., 17 (2011), 241.  doi: 10.1515/JAA.2011.015.  Google Scholar [37] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations,, Applied Mathematical Sciences, (1983).  doi: 10.1007/978-1-4612-5561-1.  Google Scholar [38] M. Renardy, On the stability of differentiability of semigroups,, Semigroup Forum, 51 (1995), 343.  doi: 10.1007/BF02573642.  Google Scholar [39] S. Taylor, Gevrey's Semigroups,, Ph.D. Thesis, (1989).   Google Scholar [40] S. Taylor, Gevrey smoothing properties of the Schrödinger evolution group in weighted Sobolev spaces,, J. Math. Anal. Appl., 194 (1995), 14.  doi: 10.1006/jmaa.1995.1284.  Google Scholar [41] V. Thomée, Galerkin Finite Element Methods for Parabolic Problems,, Second edition. Springer Series in Computational Mathematics, (2006).   Google Scholar [42] R. Triggiani, Wave equation on a bounded domain with boundary dissipation: an operator approach,, In: Operator methods for optimal control problems, 108 (1987), 283.   Google Scholar [43] R. P. Vito and S. A. Dixon, Blood Vessel Constitutive Models,, Annual Review of Biomedical Engineering, 5 (2003), 413.   Google Scholar [44] T. J. Xiao and J. Liang, A solution to an open problem for wave equations with generalized Wentzell boundary conditions,, Mathematische Annalen, 327 (2003), 351.  doi: 10.1007/s00208-003-0457-2.  Google Scholar [45] T. J. Xiao and J. Liang, Complete second order differential equations in Banach spaces with dynamic boundary condition,, J. Differential Equations, 200 (2004), 105.  doi: 10.1016/j.jde.2004.01.011.  Google Scholar [46] T. J. Xiao and J. Liang, Second order parabolic equations in Banach spaces with dynamic boundary conditions,, Trans. Amer. Math. Soc., 356 (2004), 4787.  doi: 10.1090/S0002-9947-04-03704-3.  Google Scholar

show all references

##### References:
 [1] B. Andràs and K. J Engel, Abstract wave equations with generalized Wentzell boundary conditions,, Journal of Differential Equations, 207 (2004), 1.  doi: 10.1016/j.jde.2003.12.005.  Google Scholar [2] W. Arendt and C. J. K. Batty, Tauberian theorems and stability of one-parameter semigroups,, Trans. Amer. Math. Soc., 306 (1988), 837.  doi: 10.1090/S0002-9947-1988-0933321-3.  Google Scholar [3] G. Avalos and I. Lasiecka, The strong stability of a semigroup arising from a coupled hyperbolic/parabolic system,, Semigroup Forum, 57 (1998), 278.  doi: 10.1007/PL00005977.  Google Scholar [4] G. Avalos and D. Toundykov, Boundary stabilization of structural acoustic interactions with interface on a Reissner-Mindlin plate,, Nonlinear Anal. Real World Appl., 12 (2011), 2985.  doi: 10.1016/j.nonrwa.2011.05.001.  Google Scholar [5] J. T. Beale and S. I. Rosencrans, Acoustic boundary conditions,, Bull. Amer. Math. Soc., 80 (1974), 1276.  doi: 10.1090/S0002-9904-1974-13714-6.  Google Scholar [6] J. T. Beale, Spectral properties of an acoustic boundary condition,, Indiana Univ. Math. J., 25 (1976), 895.  doi: 10.1512/iumj.1976.25.25071.  Google Scholar [7] J. T. Beale, Acoustic scattering from locally reacting surfaces,, Indiana Univ. Math. J., 26 (1977), 199.  doi: 10.1512/iumj.1977.26.26015.  Google Scholar [8] S. C. Brenner and L. R. Scott, The Mathematical Theory of Finite Element Methods,, Texts in Applied Mathematics, (1994).   Google Scholar [9] A. Borichev and Y. Tomilov, Optimal polynomial decay of functions and operator semigroups,, Math. Ann., 347 (2010), 455.  doi: 10.1007/s00208-009-0439-0.  Google Scholar [10] S. Čanić and A. Mikelić, Effective equations modeling the flow of a viscous incompressible fluid through a long elastic tube arising in the study of blood flow through small arteries,, SIAM J. Appl. Dyn. Syst., 2 (2003), 431.  doi: 10.1137/S1111111102411286.  Google Scholar [11] S. P. Chen and R. Triggiani, Proof of extensions of two conjectures on structural damping for elastic systems,, Pacific J. Math., 136 (1989), 15.  doi: 10.2140/pjm.1989.136.15.  Google Scholar [12] A. Favini, G. R. Goldstein, J. A. Goldstein and S. Romanelli, The heat equation with generalized Wentzell boundary condition,, Journal of Evolution Equations, 2 (2002), 1.  doi: 10.1007/s00028-002-8077-y.  Google Scholar [13] A. Favini, C. Gal, G. R. Goldstein, J. A. Goldstein and S. Romanelli, The non-autonomous wave equation with general Wentzell boundary conditions,, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 135 (2005), 317.  doi: 10.1017/S0308210500003905.  Google Scholar [14] A. Favini, G. R. Goldstein, J. A. Goldstein, E. Obrecht and S. Romanelli, Elliptic operators with general Wentzell boundary conditions, analytic semigroups and the angle concavity theorem,, Math. Nachr., 283 (2010), 504.  doi: 10.1002/mana.200910086.  Google Scholar [15] B. Friedman, Principles and Techniques of Applied Mathematics,, John Wiley & Sons, (1956).   Google Scholar [16] C. Gal, G. R. Goldstein and J. A. Goldstein, Oscillatory boundary conditions for acoustic wave equations,, Journal of Evolution Equations, 3 (2003), 623.  doi: 10.1007/s00028-003-0113-z.  Google Scholar [17] S. Gerbi and B. Said-Houari, Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions,, Nonlinear Anal., 74 (2011), 7137.  doi: 10.1016/j.na.2011.07.026.  Google Scholar [18] S. Gerbi and B. Said-Houari, Local existence and exponential growth for a semilinear damped wave equation with dynamic boundary conditions,, Adv. Differential Equations, 13 (2008), 1051.   Google Scholar [19] P. J. Graber and B. Said-Houari, Existence and asymptotic behavior of the wave equation with dynamic boundary conditions,, Appl. Math. Optim., 66 (2012), 81.  doi: 10.1007/s00245-012-9165-1.  Google Scholar [20] P. J. Graber, Uniform boundary stabilization of a wave equation with nonlinear acoustic boundary conditions and nonlinear boundary damping,, Journal of Evolution Equations, 12 (2012), 141.  doi: 10.1007/s00028-011-0127-x.  Google Scholar [21] A. Haraux and M. Otani, Analyticity and regularity for a class of second order evolution equations,, Evolution Equations and Control Theory, 2 (2013), 101.  doi: 10.3934/eect.2013.2.101.  Google Scholar [22] M. A. Horn and W. Littman, Local smoothing properties of a Schrödinger equation with nonconstant principal part,, In: Modelling and optimization of distributed parameter systems, (1996), 104.   Google Scholar [23] M. A. Horn and W. Littman, Boundary control of a Schrödinger equation with nonconstant principal part,, In: Control of partial differential equations and applications, 174 (1996), 101.   Google Scholar [24] J. Lagnese, Decay of solutions of wave equations in a bounded region with boundary dissipation,, J. Differential Equations, 50 (1983), 163.  doi: 10.1016/0022-0396(83)90073-6.  Google Scholar [25] W. Littman, The wave operator and $L_p$ norms,, J. Math. Mech., 12 (1963), 55.   Google Scholar [26] W. Littman and L. Markus, Exact boundary controllability of a hybrid system of elasticity,, Archive for Rational Mechanics and Analysis, 103 (1988), 193.  doi: 10.1007/BF00251758.  Google Scholar [27] W. Littman and L. Markus, Stabilization of a hybrid system of elasticity by feedback boundary damping,, Annali di Matematica Pura ed Applicata, 152 (1988), 281.  doi: 10.1007/BF01766154.  Google Scholar [28] W. Littman and S. Taylor, Smoothing evolution equations and boundary control theory,, J. Anal. Math., 59 (1992), 117.  doi: 10.1007/BF02790221.  Google Scholar [29] W. Littman and S. Taylor, Local smoothing and energy decay for a semi-infinite beam pinned at several points, and applications to boundary control,, In: Differential equations, 152 (1994), 683.   Google Scholar [30] W. Littman and B. Liu, On the spectral properties and stabilization of acoustic flow,, SIAM J. Appl. Math., 59 (1999), 17.  doi: 10.1137/S0036139996314106.  Google Scholar [31] W. Littman and S. Taylor, The heat and Schrödinger equations: Boundary control with one shot,, In: Control Methods in PDE-dynamical Systems, 426 (2007), 293.  doi: 10.1090/conm/426/08194.  Google Scholar [32] G. Lumer and R. S. Phillips, On the spectral properties and stabilization of acoustic flow,, Pacific J. Math., 11 (1961), 679.  doi: 10.2140/pjm.1961.11.679.  Google Scholar [33] T. Meurer and A. Kugi, Tracking control design for a wave equation with dynamic boundary conditions modeling a piezoelectric stack actuator,, International Journal of Robust and Nonlinear Control, 21 (2011), 542.  doi: 10.1002/rnc.1611.  Google Scholar [34] P. M. Morse and K. U. Ingard, Theoretical Acoustics,, Princeton University Press, (1987).   Google Scholar [35] D. Mugnolo, Abstract wave equations with acoustic boundary conditions,, Math. Nachr., 279 (2006), 299.  doi: 10.1002/mana.200310362.  Google Scholar [36] D. Mugnolo, Damped wave equations with dynamic boundary conditions,, J. Appl. Anal., 17 (2011), 241.  doi: 10.1515/JAA.2011.015.  Google Scholar [37] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations,, Applied Mathematical Sciences, (1983).  doi: 10.1007/978-1-4612-5561-1.  Google Scholar [38] M. Renardy, On the stability of differentiability of semigroups,, Semigroup Forum, 51 (1995), 343.  doi: 10.1007/BF02573642.  Google Scholar [39] S. Taylor, Gevrey's Semigroups,, Ph.D. Thesis, (1989).   Google Scholar [40] S. Taylor, Gevrey smoothing properties of the Schrödinger evolution group in weighted Sobolev spaces,, J. Math. Anal. Appl., 194 (1995), 14.  doi: 10.1006/jmaa.1995.1284.  Google Scholar [41] V. Thomée, Galerkin Finite Element Methods for Parabolic Problems,, Second edition. Springer Series in Computational Mathematics, (2006).   Google Scholar [42] R. Triggiani, Wave equation on a bounded domain with boundary dissipation: an operator approach,, In: Operator methods for optimal control problems, 108 (1987), 283.   Google Scholar [43] R. P. Vito and S. A. Dixon, Blood Vessel Constitutive Models,, Annual Review of Biomedical Engineering, 5 (2003), 413.   Google Scholar [44] T. J. Xiao and J. Liang, A solution to an open problem for wave equations with generalized Wentzell boundary conditions,, Mathematische Annalen, 327 (2003), 351.  doi: 10.1007/s00208-003-0457-2.  Google Scholar [45] T. J. Xiao and J. Liang, Complete second order differential equations in Banach spaces with dynamic boundary condition,, J. Differential Equations, 200 (2004), 105.  doi: 10.1016/j.jde.2004.01.011.  Google Scholar [46] T. J. Xiao and J. Liang, Second order parabolic equations in Banach spaces with dynamic boundary conditions,, Trans. Amer. Math. Soc., 356 (2004), 4787.  doi: 10.1090/S0002-9947-04-03704-3.  Google Scholar
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The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H. If the total number of rooms at Hotel G and Hotel H is 425, what is the number of rooms at Hotel G?

(A) 140
(B) 180
(C) 200
(D) 240
(E) 280

Problem Solving
Question: 13
Category: Algebra Simultaneous equations
Page: 63
Difficulty: 600

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Re: The number of rooms at Hotel G is 10 less than twice the num  [#permalink]

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30 Dec 2013, 06:00
1
SOLUTION

The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H. If the total number of rooms at Hotel G and Hotel H is 425, what is the number of rooms at Hotel G?

(A) 140
(B) 180
(C) 200
(D) 240
(E) 280

The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H --> G = 2H - 10;
The total number of rooms at Hotel G and Hotel His 425 --> G + H = 425.

Solving gives G = 280.

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Re: The number of rooms at Hotel G is 10 less than twice the num  [#permalink]

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30 Dec 2013, 23:37
2
Let G be the no. of rooms at hotel G and H be the no. of rooms at hotel H.

G = 2H - 10;
G + H = 425; H = 425 - G;

Since we have to find G,
G = 2H - 10 = 2(425 - G) - 10
G = 850 - 2G - 10;
3G = 840;
G = 840/3
G = 280;

Ans is (E).
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Re: The number of rooms at Hotel G is 10 less than twice the num  [#permalink]

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31 Dec 2013, 00:23
1
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H. If the total number of rooms at Hotel G and Hotel His 425, what is the number of rooms at Hotel G?

(A) 140
(B) 180
(C) 200
(D) 240
(E) 280

Problem Solving
Question: 13
Category: Algebra Simultaneous equations
Page: 63
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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A very good contender for back solving. Let us start with option C.

Hotel G Hotel H Total
(A) 140
(B) 180
(C) 200 210/2 = 105 200 + 105 = 305
(D) 240
(E) 280

We were supposed to get 425 however we got 305 hence we should move down

Hotel G Hotel H Total
(A) 140
(B) 180
(C) 200 210/2 = 105 200 + 105 = 305
(D) 240
(E) 280 290/2 = 145 280 + 145 = 425 (BINGO!)

Pushpinder Gill
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Re: The number of rooms at Hotel G is 10 less than twice the num  [#permalink]

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31 Dec 2013, 10:34
1
CrackVerbalGMAT wrote:
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H. If the total number of rooms at Hotel G and Hotel His 425, what is the number of rooms at Hotel G?

(A) 140
(B) 180
(C) 200
(D) 240
(E) 280

Problem Solving
Question: 13
Category: Algebra Simultaneous equations
Page: 63
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

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2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
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A very good contender for back solving. Let us start with option C.

Hotel G Hotel H Total
(A) 140
(B) 180
(C) 200 210/2 = 105 200 + 105 = 305
(D) 240
(E) 280

We were supposed to get 425 however we got 305 hence we should move down

Hotel G Hotel H Total
(A) 140
(B) 180
(C) 200 210/2 = 105 200 + 105 = 305
(D) 240
(E) 280 290/2 = 145 280 + 145 = 425 (BINGO!)

Pushpinder Gill

The solution looks very elegant.

Do you advise to start back solving from Option (E), since G/(G+H) is close to 2/3 or, the solution is approximately close to $$2/3(425)$$
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Re: The number of rooms at Hotel G is 10 less than twice the num  [#permalink]

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01 Jan 2014, 23:20
arunspanda wrote:
CrackVerbalGMAT wrote:
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H. If the total number of rooms at Hotel G and Hotel His 425, what is the number of rooms at Hotel G?

(A) 140
(B) 180
(C) 200
(D) 240
(E) 280

Problem Solving
Question: 13
Category: Algebra Simultaneous equations
Page: 63
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

A very good contender for back solving. Let us start with option C.

Hotel G Hotel H Total
(A) 140
(B) 180
(C) 200 210/2 = 105 200 + 105 = 305
(D) 240
(E) 280

We were supposed to get 425 however we got 305 hence we should move down

Hotel G Hotel H Total
(A) 140
(B) 180
(C) 200 210/2 = 105 200 + 105 = 305
(D) 240
(E) 280 290/2 = 145 280 + 145 = 425 (BINGO!)

Pushpinder Gill

The solution looks very elegant.

Do you advise to start back solving from Option (E), since G/(G+H) is close to 2/3 or, the solution is approximately close to $$2/3(425)$$

I would advise you to start with option C and then move up or down according to the condition as the answer options are always in ascending or descending order.
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Re: The number of rooms at Hotel G is 10 less than twice the num  [#permalink]

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02 Jan 2014, 02:44
1
The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H. If the total number of rooms at Hotel G and Hotel His 425, what is the number of rooms at Hotel G?

(A) 140
(B) 180
(C) 200
(D) 240
(E) 280

Sol: Let no. of room in Hotel H be X. Then No. of rooms in Hotel G is 10 less than twice the no. of rooms at Hotel H i.e No. of rooms =2X-10
Given
X+2X-10=425 or 3x=435 X=145---->No. of rooms in Hotel H
Hotel G = 2*145-10= 280
Ans E
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Re: The number of rooms at Hotel G is 10 less than twice the num  [#permalink]

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16 Jan 2018, 17:53
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H. If the total number of rooms at Hotel G and Hotel H is 425, what is the number of rooms at Hotel G?

(A) 140
(B) 180
(C) 200
(D) 240
(E) 280

We can let the number of rooms in hotel G = g and the number of rooms in hotel H = h and create the two equations:

g = 2h - 10

and

g + h = 425

Substituting the first equation for g in the second equation, we have:

2h - 10 + h = 425

3h = 435

h = 145

So g = 2(145) - 10 = 280.

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Re: The number of rooms at Hotel G is 10 less than twice the num  [#permalink]

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17 Jan 2018, 07:39
Top Contributor
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H. If the total number of rooms at Hotel G and Hotel H is 425, what is the number of rooms at Hotel G?

(A) 140
(B) 180
(C) 200
(D) 240
(E) 280

We can also solve the question using 1 variable

Let x = number of rooms at Hotel H

The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H
So, 2x - 10 = number of rooms at Hotel G

The total number of rooms at Hotel G and Hotel H is 425
We can write: x + (2x - 10) = 425
Simplify: 3x - 10 = 425
Solve: x = 145

2x - 10 = number of rooms at Hotel G
So, the number of rooms at Hotel G = 2(145) - 10
= 280

Cheers,
Brent
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The number of rooms at Hotel G is 10 less than twice the num  [#permalink]

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15 Sep 2019, 03:32
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H. If the total number of rooms at Hotel G and Hotel H is 425, what is the number of rooms at Hotel G?

(A) 140
(B) 180
(C) 200
(D) 240
(E) 280

Problem Solving
Question: 13
Category: Algebra Simultaneous equations
Page: 63
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

Given:
1. The number of rooms at Hotel G is 10 less than twice the number of rooms at Hotel H.
2. The total number of rooms at Hotel G and Hotel H is 425

Asked: What is the number of rooms at Hotel G?

Let the number of rooms at hotel G be g and at hotel H be h.
g = 2h -10 ; $$h = \frac{g+10}{2}$$. (1)
g + h = 425 (2)
$$g + \frac{g + 10}{2} = 425$$
3g + 10 = 850
g = 840/3 = 280

IMO E
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The number of rooms at Hotel G is 10 less than twice the num   [#permalink] 15 Sep 2019, 03:32
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text:
# Identify unique Verbal Arithmetic Puzzles

I am attempting to create original Verbal Arithmetic puzzles such as the famous one from this question Alphametic (Verbal Arithmetic) general strategy :

SEND+MORE=MONEY

For these problems each letter represents a different one digit number but the equation still holds true. The first letter (M or S in this case) cannot be 0 of course as that would mean they would be omitted.

My main issue with creating new ones is that most of the puzzles I develop have more than 1 solution. For example, there are 3 correct and distinct solutions to:

TWO x SIX = TWELVE

In this case, I can reduce this to one answer by making it a long multiplication problem with marked blank areas for where digits are needed but this sort of ruins the problem. My question, therefore, is what strategies can I use to develop original, unique verbal arithmetic problems that only have one possible solution?

Edit: Can anyone think of any strategies for designing the puzzles, rather than just creating them and testing for the existance of solutions and uniqueness, as suggested by Ross Millican's answer below?

• How do you solve it? Usually you solve such a puzzles starting from some letters, knowing basic Rules (like shown here: puzzling.stackexchange.com/a/52/28 ) you can find one number, then the other one, ... and all of them. To create such a puzzle you should chose the Rules you want the solver to apply and think backwards. (Then you will need to change letters in such a way that you'll get words out of numbers). – klm123 Jun 4 '14 at 18:57

I would write a program that checks these for answers. As $10!=3,628,800$ is small, it will be able to check any puzzle instantly. You have to decide what forms you want it to do. Then for ones like $TWO \times SIX = TWELVE$ you have have a calling program that goes through the multiplication table, or you can have one that does partitions checking $ONE+FOUR=FIVE$ or $ONE + FOUR+ FOUR=NINE$, first checking that the number of letters is acceptable, then checking for a solution.


text:
## Tuesday, July 31, 2012

### Hacking the Sudoku solver from The Ruby Programming Language

On only page 18 of Flanagan and Matsumoto's excellent "The Ruby Programming Language" a relatively complex example is presented: a Sudoku puzzle solver. I've had a decades-long interest in maze solvers, and this tied in nicely with that. I resolved to give the code a close look when I'd finished the book.

And surprising myself, I soon did. I read it cover-to-cover, frequently even re-reading sections I'd already covered when a lack of mastery of specific material became evident later. The language is a nice alternative to Perl, which had been my scripting language of choice since 1998. Ruby has a lot of cool characteristics, even if it sometimes falls weakness to Perl's desire to appease too much diversity in coding styles. I personally think being able to do things effectively two different ways is inferior to being able to do things as effectively only one, as the latter makes multi-author code easier to follow and coherently maintain. But as usual, I digress.

When I'd felt I'd given enough attention to the rest of the text, I returned to the Sudoku solver. I couldn't resist making some on-the-fly changes immediately. Ffor example, certain look-up tables are hard-coded when they can be trivially generated algorithmically, for example a table to the "box number" associated with a given cell. But beyond that, I didn't like that the code was hard-coded for a 9×9 puzzle. Sudokus must be a square array of squares, so the length must equal the width each of which is the square of an integer. This integer I call the "size" of the puzzle. So a 9×9 would be a size 3.

9×9 is convenient because squares can be filled with the symbols 1, 2, 3, 4, 5, 6, 7, 8, and 9. I say "symbols" rather than "numbers" because there's nothing numerical about Sudoku. The only test of the elements is the test of uniqueness. Any set of characteristics which could be tested for uniqueness could do. You can use letters, pictograms, colors, anything which can be compared for match or no match. So it's commonly stated that Sudoku is a mathematical puzzle, but the only mathematics involved are the mathematics of sets. The elements of the set are arbitrary.

Given this, I was surprised that the example puzzle begins by converting the symbols in the puzzle into integers using an obscure string of numbers stores in a string. Mappingf character sequences to integer representation is an efficiency already taken care of by the symbol object in Ruby. This approach seems more appropriate for C code than Ruby. Instead of storing cell contents with numbers and converting to strings, I converted the code to use symbols, which I store in an array. This is much simpler. The only question is what symbols to use. I picked digits 1-9 followed by letters (A-Z, then a-z) then on to circled numbers available in Unicode. This allowed me to solve puzzles up to at least 100×100 (size 10). An alternate would be to allow users of the puzzle "class" to specify the symbols to be used.

Then there was the issue of how the class was organized. A Sudoku module was defined with a puzzle "class", then a module method was defined to solve the puzzle. This seemed artificial to me, since the class had specific functionality required to support the solution algorithm, why act as if the solution was some sort of client of a more general class? I instead incorporated the solution method directly into the class, formalizing the justification for the class methods specific to the solution algorithm.

So with the code now supporting arbitrary puzzle sizes, I gave it a try. 9×9: no problem. It blows through those, even for a starting puzzle which is a totally blank board. Then 16×16 was also no problem. But get up to 25×25 and it started to develop hic-cups... and 36×36 was a real challenge.

These large puzzles revealed some more fundamental weaknesses of the original code. Here's a general outline of the algorithm:

1. If there's any squares with no options, the puzzle is impossible, so indicate that.
2. If there's a square which has only one option, choose that option, and return to the previous step (making sure the puzzle isn't impossible).
3. At this step, every blank square has at least two options. Pick one of those with the least number of options. Think of this as the square most likely to yield a correct "guess". Pick one of the available options for this square (original code picked the lowest-value option; in my code I randomize the selection order).
4. Try to solve the puzzle with the "guess" in this square. If it fails, try the next guess. If there's no more guesses available for this square, if all have been tried and each yielded an impossible puzzle, then mark the puzzle as impossible.

This algorithm naturally lends itself to recursion, so that's what Flanagan and Matsumoto do. Everytime a guess is made at a cell value, the solution method calls itself with a full copy of the puzzle with the guess filled in. Unfortunately, a large puzzle can involve a LOT of guesses. Making a full copy of the puzzle for a recursion call every time is inefficient.

So I changed this to a hierarchical data structure. Every time a guess was made only the new cell's value was stored, in a hash. If a value wasn't found in the hash, it was checked for in a parent hash from the solution call which recursively called the present one. Now memory wasn't a problem, but cell value lookups really slowed things down.

The approach I took was to have the code cache these value look-ups. Furthermore, instead of evaluating from scratch what values were unused in each row, column, and box, I stored these values in separate hashes. With this combination, memory use was substantially reduced while decent speed was restored.

A problem remained however, and that was stack size. LISP is a language in which recursion is a preferred technique: the language is designed with what's called "tail recursion" so that recursion can be done efficiently. Ruby doesn't have this -- it's optimized for loops, not recursion. I was hitting fundamental stack limits with the larger puzzles for which there seemed to be no solution.

So I decided to bite the bullet and get rid of the recursion. Recursion is super-convenient for book-keeping. Eliminating the recursion required that I keep track of where I was, where I was, and how to get back to previous states if the present solution direction yielded a dead end. Eventually I got it working, but only with considerable effort.

Now once again I had no problem with the smaller puzzles. But I really wanted to solve 36×36 and beyond. In these puzzles, the code would get hung up for many hours, seemingly stuck in a loop. But from the algorithm, a loop should be impossible... to check for this, I installed code which kept a record of a "hash value" for a puzzle state, then checking to make sure no solution loops were found. I'd check for loops up to 10 thousand steps long, and never found any. Yet the solution would grind on for 10 million total guesses or more...

I retreated to smaller puzzles. Generally the code could solve these, but every often it would get hung up. It would grind on and on, modifying a small group of squares in an attempt to break through to a solution path. Once the path was found, the rest of the solution might go quickly.

The issue is Sudoku puzzles are like mazes, but in solving mazes, the number of options available at a given point is at most 2×N, where N is the number of dimensions. With Sudoku there may be as many as L options available, where L is the side length of the puzzle. It's not surprising it would be easy to get lost in a 32-dimensional maze...

So I've concluded solving big Sudoku's is simply difficult. Without researching it, I wonder if it's possible to apply more intelligence to the situation than simply guessing, in order, the options of the square with the least number of options. But I'll leave it at that: my mission of exercising Ruby skills was accomplished. (note: I just noticed there's a forum dedicated to the topic!)

Finally, here's a sample of my test case. I start with a minimal puzzle, one with a single row and column randomly filled it with no box violations:

.  .  .  .  .  .  .  .  .  .  .  .  .  .  2  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  1  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  C  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  6  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  N  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  3  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  5  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  9  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  7  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  F  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  E  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  D  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  4  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  K  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  P  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  I  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  M  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  8  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  O  .  .  .  .  .  .  .  .  .  .
3  C  P  4  9  G  B  K  1  F  7  L  5  N  A  D  O  I  6  H  E  M  8  2  J
.  .  .  .  .  .  .  .  .  .  .  .  .  .  G  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  L  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  H  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  J  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  B  .  .  .  .  .  .  .  .  .  .

Then I solve. Progress is shown here, with a logarithmic axis on iteration number, where the y-axis is number of points solved (not every point is shown). You can see how the progress is in short bursts, then the solver becomes bogged down, then there's another short burst. These portions of no visible progress can last for millions of iterations if I'm unlucky.

Then here's the solution (non-unique in this case). Nodes which received at least as many guesses as total cells in the puzzle (in this case 625) are encased in [brackets]:

G  L  4  B  1  K  P  H  J  9  M  D  I  O  2  3  N  7  C  8  6  A  5  E  F
F  K  6  A  M  D  N  C  O  8  G  5  L  B  1  P  H  E  2  4  9  3  J  7  I
8  O  D  2  E  B  L  1 [5][I] H  3  7  4  C [A][6][J][9] F  M  G  N  K  P
I  N  C  3  J  E  F  G  2  7  P  8  9  A  6  M  5  L  D  K  1  H  B  4  O
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Miki said...

Hello.
Could you tell me what program do you use to make elevation profiles and other graphic?
Regards,
Michal

djconnel said...

[url=http://plasma-gate.weizmann.ac.il/Grace/]xmgrace[/url]: not so easy to use but produces good-quality plots. I wish I knew gnuplot... need to invest time in learning that at some point. It has has better default behavior and is easier to generate automatically.


text:
## Stream: new members

### Topic: Lean for Cryptography

#### Cibo (Oct 18 2019 at 10:44):

Hello,
Can you please give any references on using lean for proving security of ciphers or cryptographic protocols?
Or at least give opinion on possibility of development tools that would help with cryptography?

Im intrigued by possibility of having tool for rapid prototyping crypto primitives construction, but im curious if it be possible to express some probabilistic boundary or computation boundary?

#### Johan Commelin (Oct 18 2019 at 12:00):

@Cibo I'm not aware of any crypto written in Lean so far

#### Johan Commelin (Oct 18 2019 at 12:01):

We certainly have all the ingredients in place to implement RSA.

#### Cibo (Oct 18 2019 at 12:07):

We certainly have all the ingredients in place to implement RSA.

Thanks! Sounds like a nice challenge for a weekend

#### Johan Commelin (Oct 18 2019 at 12:22):

@Cibo You'll probably want to use mathlib. Also, I make no promises about whether the resulting code will run fast enough to work with key sizes >10.

#### Cibo (Oct 18 2019 at 12:28):

@Johan Commelin I am more interested in proving that no adversary would be able to get private key out of public key with probability grater then $\varepsilon$ within time boundary of time $t$. Rather then calculate actual ciphertexts

#### Kevin Buzzard (Oct 18 2019 at 17:45):

But there could in theory be an O(n) algorithm for factoring / breaking your favourite protocol, no?

#### Cibo (Oct 18 2019 at 18:30):

@Kevin Buzzard yes.
That is why I will have to define some assumption(like hardness of factorisation and best known attack on it). I know that there is a shores algorithm, but lets do some basics first.

I would like to end up with set of assumption and proofs s.t. any new cryptographic protocol that would be build can be easily analyzed by hardness of its assumptions(if proof holds).

My question here is: should I start learning lean or my goal is not reachable at all? and I should go back to coq, proverif and tamarin

#### Simon Hudon (Oct 18 2019 at 19:45):

@Cibo you may want to talk to @Joe Hendrix

#### Joe Hendrix (Oct 18 2019 at 20:27):

@Cibo I was involved in a project at Galois where we worked on a protocol specification, and verified some correctness properties (specified in LTL) in Lean 3. We were starting on infrastructure for cryptographic hardness proofs (I was probably going to borrow heavily from FCF), but the project needed to shift directions.
I don't see any theoretical problems in using Lean for this, and I found Lean's metaprogramming and tactic approach quite useful. However, there is relatively little in the way of existing libraries for doing this.

#### Joe Hendrix (Oct 18 2019 at 20:28):

We made all the code we can share available here: https://github.com/GaloisInc/lean-protocol-support. The use case was for a third party block chain system that I was not allowed to share, but the infrastructure is there.

#### Joe Hendrix (Oct 18 2019 at 20:30):

On the crypto side, the repo has SHA2, HMAC, and some basic Merkle tree work. It'd be neat to see more, perhaps a block cipher and public key method.

#### Cibo (Oct 18 2019 at 21:32):

Many thanks @Simon Hudon, @Joe Hendrix ! :big_smile:

Last updated: May 09 2021 at 18:17 UTC


text:
# Hamilton Path properties

As I understand a graph has a Hamilton Circuit if

• It has $n \ge 3$ vertexes
• degree of every vertex is at least $n/2$
• $\deg u + \deg v \ge n$ for every pair of nonadjacent vertices $u$ and $v$ in the graph

I can't seem to find a concrete set of properties for deciding if a graph has a Hamilton Path. Can anyone help me out? Please add some references/sources :)

-
Note that these conditions are sufficient, but not necessary. A regular hexagon fails the second two, but has a Hamiltonian path. –  Ross Millikan Jul 27 '11 at 22:02
You're stating Ore's theorem (but your second condition is not needed): en.wikipedia.org/wiki/Ore_theorem –  Justin W Smith Jul 28 '11 at 4:40

A number of sufficient conditions can be found in this thesis of Landon Jennings, among them Chvátal’s condition: if $d_1 \le d_2 \le \dots \le d_n$ are the degrees of $G$, and for $1 \le k \le n/2$ either $d_k \ge k$ or $d_{n+1-k} \ge n-k$, then $G$ has a Hamilton path. The main result of the thesis is the following. Let $G$ be a connected graph with degree sequence $d_1 \le d_2 \le \dots \le d_n$, and let $A(G)$ be the largest integer $k$ such that $\sum\limits_{i=1}^k d_k \le |E(G)|$; if $d_2 \ge A(G)-1$, then $G$ contains a Hamilton path. This test detects some graphs with Hamilton paths not detected by Chvátal’s condition. Some of the references may also be useful.
As stated above, all graphs that contain hamiltonian cycles contain hamiltonian paths, however, this does not capture all graphs that have paths but not cycles. As a simple example consider $P_n$. Also, any connected graph, not isomorphic to $C_n$ where each vertex sits on 1 cycle contains a hamiltonian path but not a hamiltonian cycle. Finally, a connected graph that contains a spanning tree with 2 and only 2 vertices of degree 1 has a hamiltonian path but not a hamiltonian cycle.


text: 2. What is meant by choosing a suitable partition? Just integrating directly shows that the inequality is true since $\displaystyle 3.5\leq 3.75\leq 4$