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# TTE Data¶

TTE (Time-Tagged Event) data is basically a time-series of “counts” where each count is mapped to an energy channel. It is basically the temporally unbinned representation of CSPEC data (128 energy channels). We can read a TTE file much the same way we can read a CTIME or CSPEC file.

[1]:

from gbm import test_data_dir
# import the TTE data class
from gbm.data import TTE

# read a tte file
tte = TTE.open(test_data_dir+'/glg_tte_n9_bn090131090_v00.fit')
print(tte)

glg_tte_n9_bn090131090_v00.fit

Similar to the other datatypes, TTE data are stored in FITS files, and so all the metadata in the headers can be accessed:

[2]:

# list the headers in the file

[2]:

odict_keys(['PRIMARY', 'EBOUNDS', 'EVENTS', 'GTI'])

[3]:

# print the metadata in the PRIMARY header

[3]:

SIMPLE  =                    T / file does conform to FITS standard
BITPIX  =                    8 / number of bits per data pixel
NAXIS   =                    0 / number of data axes
EXTEND  =                    T / FITS dataset may contain extensions
COMMENT   FITS (Flexible Image Transport System) format is defined in 'Astronomy
COMMENT   and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H
CREATOR = 'GBM_TTE_Reader.pl v2.8' / Software and version creating file
FILETYPE= 'GBM PHOTON LIST'    / Name for this type of FITS file
FILE-VER= '1.0.0   '           / Version of the format for this filetype
TELESCOP= 'GLAST   '           / Name of mission/satellite
INSTRUME= 'GBM     '           / Specific instrument used for observation
DETNAM  = 'NAI_09  '           / Individual detector name
OBSERVER= 'Meegan  '           / GLAST Burst Monitor P.I.
ORIGIN  = 'GIOC    '           / Name of organization making file
DATE    = '2009-01-31T04:55:38' / file creation date (YYYY-MM-DDThh:mm:ss UT)
DATE-OBS= '2009-01-31T02:08:57' / Date of start of observation
DATE-END= '2009-01-31T02:14:23' / Date of end of observation
TIMESYS = 'TT      '           / Time system used in time keywords
TIMEUNIT= 's       '           / Time since MJDREF, used in TSTART and TSTOP
MJDREFI =                51910 / MJD of GLAST reference epoch, integer part
MJDREFF = 7.428703703703703D-4 / MJD of GLAST reference epoch, fractional part
TSTART  =     255060537.657974 / [GLAST MET] Observation start time
TSTOP   =     255060863.884596 / [GLAST MET] Observation stop time
FILENAME= 'glg_tte_n9_bn090131090_v00.fit' / Name of this file
DATATYPE= 'TTE     '           / GBM datatype used for this file
TRIGTIME=     255060563.149072 / Trigger time relative to MJDREF, double precisi
OBJECT  = 'GRB090131090'       / Burst name in standard format, yymmddfff
RADECSYS= 'FK5     '           / Stellar reference frame
EQUINOX =               2000.0 / Equinox for RA and Dec
RA_OBJ  =              30.0000 / Calculated RA of burst
DEC_OBJ =              -15.000 / Calculated Dec of burst
ERR_RAD =                3.000 / Calculated Location Error Radius
INFILE01= 'glg_lutcs_nai_090122805_v00.fit' / Level 1 input lookup table file
INFILE02= 'GLAST_2009031_042300_VC09_GBTTE.0.00' / Level 0 input data file
CHECKSUM= 'MePaNZNUMbNZMZNZ'   / HDU checksum updated 2009-01-31T04:55:40
DATASUM = '         0'         / data unit checksum updated 2009-01-31T04:55:38

There is also easy access for certain important properties:

[4]:

# certain useful properties are easily accessible
print("GTI: {}".format(tte.gti))
print("Trigger time: {}".format(tte.trigtime))
print("Time Range: {}".format(tte.time_range))
print("Energy Range: {}".format(tte.energy_range))
print('# of Energy Channels: {}'.format(tte.numchans))

GTI: [[-25.49109798669815, 300.73552399873734]]
Trigger time: 255060563.149072
Time Range: (-25.49109798669815, 300.73552399873734)
Energy Range: (4.3897295, 2000.0)
# of Energy Channels: 128

The TTE data class is modeled as a wrapper around the EventList Data Primitive in gbm.data.primitives, and the underlying data can be accessed via the .data attribute:

[5]:

tte.data

[5]:

<gbm.data.primitives.EventList at 0x121bb6fd0>

Most casual users need not directly worry about the EventList data primitive, though. The TTE data objects contain the high-level functionality to perform a lot of common data reduction. For example, if we only want to work with a short time segment of TTE data in the file, we can take a slice of the data and return a new fully-functional data object with the time-sliced data:

[6]:

# slice from -10 to +10 s
time_sliced_tte = tte.slice_time([-10.0, 10.0])
print(time_sliced_tte.time_range)

(-9.999035984277725, 9.998922020196915)

And you can slice in energy:

[7]:

# slice from ~50 keV to ~300 keV
energy_sliced_tte = tte.slice_energy((50.0, 300.0))
print(energy_sliced_tte.energy_range)

(48.08033, 304.68533)

Making a lightcurve using TTE data is slightly more complicated than it is for the pre-binned data because the TTE is temporally unbinned. So first the data has to be binned, and then it can be displayed. On the CTIME/CSPEC page, we were briefly introduced to the capability of rebinning pre-binned data. Here, we want to bin unbinned data. In the gbm.binning module, there are two sub-modules containing various binning algorithms, one for pre-binned data, the other for unbinned data. We should choose the sub-module that is appropriate for the data that we are using.

[8]:

# import the bin_by_time algorithm for unbinned data
# This function is the unbinned equivalent of gbm.binning.binned.rebin_by_time
from gbm.binning.unbinned import bin_by_time

Once we’ve identified the binning algorithm we want to use, then we can convert our TTE data object to a PHAII object similar to CTIME/CSPEC:

[9]:

# bin TTE to 1.024 s resolution.
# time_ref is the reference time for binning;
# if not set, it will bin starting at the beginning of the data
phaii = tte.to_phaii(bin_by_time, 1.024, time_ref=0.0)
type(phaii)

[9]:

gbm.data.phaii.Cspec

Well that’s cool, but why is it a Cspec object now? It’s Cspec because TTE has 128 energy channels, just like CSPEC. We’ll see what the spectrum looks like in a sec. But first, let’s look at the lightcurve. Since it’s a PHAII object, we can make a lightcurve plot the same way we would make one using pre-binned data:

[10]:

%matplotlib inline
import matplotlib.pyplot as plt
from gbm.plot import Lightcurve

lcplot = Lightcurve(data=phaii.to_lightcurve())
plt.show()

A nice looking GRB! Now if you wanted to rebin the data, you could certainly rebin the PHAII object, but if you want to leverage the full power and flexibility of TTE, it would be good to (re)bin the TTE data using the algorithm and settings of your choice.

To plot the spectrum, we don’t have to worry about binning the data, since the TTE is already necessarily pre-binned in energy. So we can make a spectrum plot the same way we make one for CTIME/CSPEC without any extra steps:

[11]:

from gbm.plot import Spectrum

# integrate over time from 0-10 s
spectrum = tte.to_spectrum(time_range=(0.0, 10.0))

specplot = Spectrum(data=spectrum)
plt.show()

A very nice count spectrum, certainly much prettier than the CTIME spectrum! Note that this is integrated over the full time range of the data. Perhaps the spectral resolution is a little bit higher than you care for (i.e. studying a weak source). You can rebin the count spectrum, but remember that the energy is pre-binned, so you need to use the appropriate class of algorithms:

[12]:

from gbm.binning.binned import combine_by_factor

# rebin the count spectrum by a factor of 4
rebinned_energy = tte.rebin_energy(combine_by_factor, 4)

rebinned_spectrum = rebinned_energy.to_spectrum(time_range=(0.0, 10.0))
specplot = Spectrum(data=rebinned_spectrum)
plt.show()

As with the pre-binned types, we can convert one or more time selections to a single spectrum PHA object. You can do this from TTE without having to bin in time:

[13]:

# create a PHA object by integrating over 0-10 s and 30-50 s
pha = tte.to_pha(time_ranges=[(0.0, 10.0), (30.0, 50.0)])

Sometimes, you might want to save snippets of TTE, or even merge your TTE snippets into one file and write it to file for later. Guess what? You can do that, too:

[14]:

time_sliced_tte2 = tte.slice_time([30.0, 50.0])

# merge our new time slice with the time slice we made earlier
tte_slices_merged = TTE.merge([time_sliced_tte, time_sliced_tte2])
tte_slices_merged.time_range

[14]:

(-9.999035984277725, 49.99965399503708)

And then you can write it as a fully-qualified TTE FITS file using

tte_slices_merged.write('./', filename='my_first_custom_tte.fit')

You’ve just learned all about the primary GBM Science Data! Follow on to learn about the GBM detector response files


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## 8.93

$w=-P\Delta V$
and
$w=-\int_{V_{1}}^{V_{2}}PdV=-nRTln\frac{V_{2}}{V_{1}}$

Janine Chan 2K
Posts: 71
Joined: Fri Sep 29, 2017 7:04 am

### 8.93

When writing the chemical equation, how do you know water is in the liquid state?

Johann Park 2B
Posts: 51
Joined: Thu Jul 27, 2017 3:01 am
Been upvoted: 1 time

### Re: 8.93

The problem states that this is a combustion reaction at 25°C. The two products that come from combustion are CO2(g) and H2O - the H2O is liquid water because the combustion happens at room temperature.

Charles Ang 1E
Posts: 50
Joined: Thu Jul 13, 2017 3:00 am

### Re: 8.93

The reaction takes place at room temperature, and water at room temperature is liquid.

Posts: 60
Joined: Thu Jul 13, 2017 3:00 am
Been upvoted: 1 time

### Re: 8.93

when its a combustion reaction, I generally assume the water is in a liquid state.

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text:
# Field of definition of Galois representations of weight 1 modular forms

Let $f$ be a weight 1 modular form (let's say cuspidal, new, normalized, and a Hecke eigenform). Then there's an associated Artin representation $\rho_f: \operatorname{Gal}(\overline{\mathbf{Q}} / \mathbf{Q}) \to GL_2(\mathbf{C})$.

The character of this representation is determined by $f$, so it takes values in the number field $L = \mathbf{Q}(a_n(f): n \ge 1)$. Are there examples where $\rho_f$ is not definable over $L$, i.e. isn't conjugate to a morphism $\operatorname{Gal}(\overline{\mathbf{Q}} / \mathbf{Q}) \to GL_2(L)$?

(There are lots of examples of even representations in the LMFDB where this happens, coming from even Artin representations with image $Q_8$ or $S_4$, but I can't find any odd ones.)

• Hi David. What is the LMFDB? – Joël Sep 11 '14 at 3:05
• L-Functions and Modular Forms Database (lmfdb.org). They have a searchable database of Artin representations, but unfortunately it doesn't seem to include Joe Buhler's example. – David Loeffler Sep 11 '14 at 3:40

No. The fact that $\rho(c)$ has eigenvalues +1 and -1 implies that $\rho$ is defined over $L$. Here is a low-tech, longish argument (there are shorter ones using slightly more technology), which is essentially from an old paper of Wiles.
Work in a basis $(e_1,e_2)$ where $\rho(c)$ is the diagonal matrix $(1,-1)$. Now let $g \in G:= Gal( \overline {\bf Q}/\bf Q)$ and write $$\rho(g)=\left(\begin{matrix} a & b \\ c & d \end{matrix}\right)$$ in the same basis. Writing that $tr\ \rho(g)$ is in $L$ gives $a+d \in L$; writing that $tr \rho(gc)$ is in $L$ gives $a-d \in L$. Hence $a,d$ are in $L$ (for all $g \in G$).
Next takes a second element $g' \in G$, and write $$\rho(g')=\left(\begin{matrix} a' & b' \\ c' & d' \end{matrix}\right),$$ so that $$\rho(gg') = \left(\begin{matrix} aa'+bc' & * \\ * & * \end{matrix}\right).$$ By the above paragraph applied to $g$, $g'$ and $gg'$, we know that $a$, $a'$ and $aa'+bc'$ are all in $L$. Thus $bc'$ is in $L$ (for all $g, g' \in G$, that is). Now we can certainly choose a $g$ such that $b \neq 0$ (otherwise $\rho$ would be reducible), and by changing the basis $(e_1,e_2)$ into $(be_1,e_2)$ (which does not affect the matrix of $\rho(c)$, hence does not affect the preceding conclusions), we may assume that $b=1$ for that $g$. We deduce that $c' \in L$ for all $g' \in G$. Next we can find a $g'\in G$ such that $c' \neq 0$, and then $bc' \in L$ implies $b \in L$. So we have shown that for all $g \in G$, all four coefficients of $\rho(g)$ are in $L$. QED.
Here is another proof of the result from Joel's answer, using a little more theory: a two dimensional irrep. of a finite group $G$ corresponds to a simple algebra factor $A$ of the group ring $\mathbb Q[G]$, where $A$ is $4$-dimensional over its centre (which is some number field $F$). Thus $A$ is either $M_2(F)$, or a non-split quat. alg. over $F$. In particular, in the second case $A$ is a division algebra.
If $c \in G$ has order $2$, with image $\bar{c}$ in $A$, then since $c^2 = 1$, we see that $(\bar{c} -1)(\bar{c} + 1) = 0$ in $A$. If $A$ is a division algebra, we conclude that either $\bar{c} = 1$ or $\bar{c} = -1$.
Thus if the image of $c$ is not scalar, we see that $A = M_2(F)$, which is to say that the given irrep. is defined over its trace field.


text:
515 - Cinematic-L1 Video Stabilization with a Log-Homography Model

# 515 - Cinematic-L1 Video Stabilization with a Log-Homography Model

Feb 04, 2021
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24 views
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###### Details
We present a method for stabilizing handheld video that simulates the camera motions cinematographers achieve with equipment like tripods, dollies, and Steadicams. We formulate a constrained convex optimization problem minimizing the $\ell_1$-norm of the first three derivatives of the stabilized motion. Our approach extends the work of Grundmann et al. [9] by solving with full homographies (rather than affinities) in order to correct perspective, preserving linearity by working in log-homography space. We also construct crop constraints that preserve field-of-view; model the problem as a quadratic (rather than linear) program to allow for an $\ell_2$ term encouraging fidelity to the original trajectory; and add constraints and objectives to reduce distortion. Furthermore, we propose new methods for handling salient objects via both inclusion constraints and centering objectives. Finally, we describe a windowing strategy to approximate the solution in linear time and bounded memory. Our method is computationally efficient, running at 300fps on an iPhone XS, and yields high-quality results, as we demonstrate with a collection of stabilized videos, quantitative and qualitative comparisons to [9] and other methods, and an ablation study.


text:
# RMO Part-5!

Number Theory Level 4

Find the sum of all integers $$n$$ such that,

$\large \frac{7n-12}{2^{n}}+\frac{2n-14}{3^{n}}+\frac{24n}{6^{n}}=1$

×


text:
• Volume 127, Issue 7

October 2018

• Evolution of Hutti-Maski greenstone belt of the Eastern Dharwar Craton: Evidence for metamorphic and hydrothermal phases from the Hira-Buddini deposit, Raichur district, Karnataka, India

The Hira-Buddini gold deposit is located along the steeply dipping ENE trending sheared contact of felsic and mafic rocks of strike length of about 600 m with mylonitic foliation parallel to the S1 schistosity in amphibolites. Second-generation open folds with axial planes (S2) marked by fractures that are often filled by later calcite veins are observed in surface and underground exposures. Garnetiferous amphibolites occur in patches on the footwall side of the shear in the western part of the deposit. This rock shows garnet porphyroblasts, coarse second-generation hornblende and large grains of biotite that grow over an early S1 fabric which is made up of early hornblende, plagioclase, ilmenite and retrograde first-generation chlorite. Second-generation hornblende and biotite grains make high angles to S1 schistosity and are sub-parallel to S2. Late hydrothermal alteration is marked by an albite-epidote-chlorite-zoisite assemblage. Geothermometric estimates based on garnet-biotite, and garnet-hornblende pairs, as well as Ti in biotite, show that temperatures during D2 deformation that led to the growth of the porphyroblasts were $530{\pm }20^{\circ }\hbox {C}$. The fabric and mineralogy of the rock indicate that porphyroblastic growth of garnet, hornblende and biotite was preceded and succeeded by stages of hydrothermal alteration. Primary gold mineralization is inferred to be associated with the early stage of hydrothermal ingress.

• Assessing the copula selection for bivariate frequency analysis based on the tail dependence test

The flood characteristics, namely, peak, duration and volume provide important information for the design of hydraulic structures, water resources planning, reservoir management and flood hazard mapping. Flood is a complex phenomenon defined by strongly correlated characteristics such as peak, duration and volume. Therefore, it is necessary to study the simultaneous, multivariate, probabilistic behaviour of flood characteristics. Traditional multivariate parametric distributions have widely been applied for hydrological applications. However, this approach has some drawbacks such as the dependence structure between the variables, which depends on the marginal distributions or the flood variables that have the same type of marginal distributions. Copulas are applied to overcome the restriction of traditional bivariate frequency analysis by choosing the marginals from different families of the probability distribution for flood variables. The most important step in the modelling process using copula is the selection of copula function which is the best fit for the data sample. The choice of copula may significantly impact the bivariate quantiles. Indeed, this study indicates that there is a huge difference in the joint return period estimation using the families of extreme value copulas and no upper tail copulas (Frank, Clayton and Gaussian) if there exists asymptotic dependence in the flood characteristics. This study suggests that the copula function should be selected based on the dependence structure of the variables. From the results, it is observed that the result from tail dependence test is very useful in selecting the appropriate copula for modelling the joint dependence structure of flood variables. The extreme value copulas with upper tail dependence have proved that they are appropriate models for the dependence structure of the flood characteristics and Frank, Clayton and Gaussian copulas are the appropriate copula models in case of variables which are diagnosed as asymptotic independence.

• Characterization of organic carbon in black shales of the Kachchh basin, Gujarat, India

Thirty-three black shale samples from four locations on the onland Kachchh basin, western India were analyzed to characterize organic carbon (OC), thermal maturity and to determine the hydrocarbon potential of the basin. Upper Jurassic black shales from the Jhuran Formation (Dhonsa and Kodki areas) are characterized by the presence of chlorite, halloysite, high $T_{\mathrm{max}}$, low OC, low hydrogen index and high oxygen index. These parameters indicate the OC as type IV kerogen, formed in a marine environment. The rocks attained thermal maturity possibly during Deccan volcanism. Early Eocene samples of the Naredi Formation (Naliya-Narayan Sarovar Road (NNSR) and the Matanomadh areas) are rich in TOC, smectite, chlorite and framboidal pyrite, but have low $T_{\mathrm{max}}$. These indicate deposition of sediments in a reducing condition, probably in a lagoonal/marsh/swamp environment. Organic carbon of the Naredi Formation of NNSR may be considered as immature type III to IV kerogen, prone to generate coal. Core samples from the Naredi Formation of the Matanomadh area show two fold distribution in terms of kerogen. Organic carbon of the upper section is immature type III to IV kerogen, but the lower section has type II to III kerogen having potential to generate oil and gas after attaining appropriate thermal maturity.

• Carbon dioxide, water vapour and energy fluxes over a semi-evergreen forest in Assam, Northeast India

The eddy covariance method is a powerful technique for quantification of $\hbox {CO}_{2}$, $\hbox {H}_{2} {\rm O}$ and energy fluxes in natural ecosystems. Leaf area index (LAI) and its changes are significant drivers of $\hbox {CO}_{2}$ and $\hbox {H}_{2}$O exchange in a forest ecosystem due to their role in photosynthesis. The present study reports the seasonal variation of $\hbox {CO}_{2}$ and energy fluxes and their relationship with other meteorological parameters of a semi-evergreen primary forest of Kaziranga National Park, Assam, India during February 2016–January 2017. The diurnal pattern of half hourly average $\hbox {CO}_{2}$ fluxes over the forest was found to be mostly dominated by the incident photosynthetically active radiation. During the period of study, diurnal variations of $\hbox {CO}_{2}$ flux showed a maximum value of $-9.97 \mu mol \hbox {m}^{-2}\hbox {s}^{-1}$ in the month of June during summer which is also the beginning of the monsoon season. The monthly averaged diurnal $\hbox {CO}_{2}$ flux and variation in LAI of the forest canopy closely followed each other. The annual net ecosystem exchange of the forest estimated from the $\hbox {CO}_{2}$ flux data above the canopy is 84.21 g C $\hbox {m}^{-2}\,\hbox {yr}^{-1}$. Further studies are in progress to confirm these findings. The estimated average annual evapotranspiration of the semi-evergreen forest is 2.8 $\pm$ 0.19 mm $\hbox {day}^{-1}$. The study of partitioning of energy fluxes showed the dominance of latent heat fluxes over sensible heat fluxes. The energy balance closure was found to increase with an increase in instability and the highest closure of around 83% was noted under neutral conditions.

• Modelling forest resilience in Hindu Kush Himalaya using geoinformation

Resilience is the capacity of an ecosystem to absorb disturbance and undergo change while maintaining its essential structure, functions, identity and feedbacks. The forests of the Hindu Kush Himalayan (HKH) region are vulnerable to both natural and anthropogenic changes, and the forest land conversion and degradation. Using satellite-derived tree canopy cover percent data and precipitation as the explaining variable, we studied the forest cover resilience in a geospatial framework employing the logistic regression and polynomial equation fitting. Out of the $4.3\,\hbox {million km}^{2}$ geographical areas, $873{,}650\,\hbox {km}^{2}$ (20.20%) was under the forest in 2000 and experienced loss of $11{,}250\,\hbox {km}^{2}$ during 2000–2010. We could model the forest cover and treeless areas fairly than the scrub and grassland owing to the variation in precipitation pattern. The majority of the forest cover (59.3%) has been estimated to have less resilience owing to the receipt of <1650 mm of total annual precipitation, whereas only $375\,\hbox {km}^{2}$ forest area could change to scrub that shows the least resilience. About 94.4% of treeless areas were estimated to be stable, while only 1% $(25{,}200\,\hbox {km}^{2})$ area could accommodate the grassland. The resilient forest areas estimated and observed, owing to the mapping and modelling protocols used in this study, shall be useful in conservation planning in the HKH region.

• Geochemistry and distribution of sediments in the East Indian shelf, SW Bay of Bengal: implications on weathering, transport and depositional environment

Forty-two substrate sediment samples and three cores procured from the shelf region between Chennai and Cuddalore were analyzed to understand the spatial and vertical sediment distribution. Samples subjected to grain size, bulk and clay mineralogical analyses, REE and trace element geochemistry yielded interesting results about the sediment characteristics with respect to the modern day environment. The present study revealed that the study area is characterized by high energy environment marked by predominant composition of medium sand. Results confirmed the evidence of more illite than kaolinite, smectite, and chlorite in the clay mineral assemblage indicating a terrigenous source. Geochemical data also revealed that the enrichment of light rare earth elements (LREE) in the sediments is due to continental source of Precambrian times. High feldspar content in the sediments which is emphasized by bulk mineralogical data displayed positive Eu anomaly. By using the paleoredox index, the area of interest is considered to have undergone no major changes in its depositional settings.

• Application of instantaneous spectral analysis and acoustic impedance wedge modeling for imaging the thin beds and fluids of fluvial sand systems of Indus Basin, Pakistan

Fluvial sand frameworks have magnificent oil and gas reservoirs far and wide. The reservoir sands are exceedingly compartmentalized by the broadened fault framework. So, to distinguish the thin beds of gas-bearing facies is an assessment for band-limited stratigraphic investigation. To conquest this issue, we execute the progressed seismic ascribe methods to the 3D seismic information of the Miano area of the Indus Basin, SW Pakistan. Apparatuses, for example, the seismic amplitude and coherence are discovered less exact for reservoir description. Sweetness analysis indicates the gas-bearing reservoir facies, which are compartmentalized by the NNW–SSE oriented normal fault system. Yet, the continuous wavelet transforms (CWT) of spectral decomposition (SD) separates the thick and thin sand beds of channel sand and point bars, which were not unsurprising utilizing the band-limited seismic properties. 22 Hz demonstrates the best amplitude tuning cube, which recognizes the profitable clastic (sand-filled barrier bars) sequences. The net-to-gross (N/G) examination uncovers the barrier bars as the chief hydrocarbon-bearing facies. 22 to 37 Hz frequencies confirm the occurrence of hydrocarbon sands. The acoustic impedance (AI) wedge model settles the thin beds of barrier bars sands, which are encased inside the shales, and affirm the suggestions for gas-bearing stratigraphic traps.

• Hydrocarbon source rock potential evaluation of the Late Paleocene Patala Formation, Salt Range, Pakistan: Organic geochemical and palynofacies approach

Organic geochemical and palynofacies analyses were carried out on shale intervals of the Late Paleocene Patala Formation at Nammal Gorge Section, western Salt Range, Pakistan. The total organic carbon content and Rock-Eval pyrolysis results indicated that the formation is dominated by type II and type III kerogens. Rock-Eval ${T}_{\mathrm{max}}$ vs. hydrogen index (HI) and thermal alteration index indicated that the analysed shale intervals present in the formation are thermally mature. $S_{1}$ and $S_{2}$ yields showed poor source rock potential for the formation. Three palynofacies assemblages including palynofacies-1, palynofacies-2 and palynofacies-3 were identified, which are prone to dry gas, wet gas and oil generation, respectively. The palynofacies assessment revealed the presence of oil/gas and gas prone type II and type III kerogens in the formation and their deposition on proximal shelf with suboxic to anoxic conditions. The kerogen macerals are dominated by vitrinite and amorphinite with minor inertinite and liptinite. The kerogen macerals are of both marine and terrestrial origin, deposited on a shallow shelf. Overall, the dark black carbonaceous shales present within the formation act as a source rock for hydrocarbons with poor-to-moderate source rock quality, while the grey shales act as a poor source rock for hydrocarbon generation.

• PSHA of Van province for performance assessment using spectrally matched strong ground motion records

Within the framework of the performance based earthquake engineering, site specific earthquake spectra for Van province has been obtained. It is noteworthy that, in probabilistic seismic hazard assessment, as a first stage data from geological studies and records from the instrumental period were compiled to make a seismic source characterization for the study region. The probabilistic seismic hazard curves were developed based on selected appropriate attenuation relationships, at rock sites, with a probability of exceedance 2, 10 and 50% in 50 yrs period. The obtained results are compared with the spectral responses proposed for seismic evaluation and retrofit of building structure in Turkish Earthquake Code (2007), section 7. The acceleration response spectrums obtained from probabilistic seismic hazard analysis are matched to adjust earthquake accelerograms recorded during the 2011 Van earthquakes by using SeismoMatch v2.0 software. The aim of this procedure is to obtain a set of reasonable earthquake input motions for the seismic evaluation of existing buildings.

• Modelling of streamflow in snow dominated Budhigandaki catchment in Nepal

This study has been envisaged to model streamflow runoff-contributed mostly by snowmelt from Budhigandaki catchment in Nepal. Available hydro-meteorological data have been collected from the Department of Hydrology and Metrology, Nepal. The MODIS Aqua (MYD10A2) and Terra (MOD10A2) 8 day maximum snow cover extent product have been used to derive the snow cover area (SCA) in the basin. The modeling of streamflow has been carried out using HEC-HMS and SRM models. The performance of these models have been evaluated by using three well known evaluation criteria NSE,${R}^{2}$ and PEV (percentage error in volume). The values of NSE, ${R}^{2}$ and PEV were found to be 0.944, 0.944 and $-0.3\%$ for SRM and 0.778, 0.785 and $-1.83\%$ for HEC-HMS, respectively. Similarly, in validation period the average values of NSE, ${R}^{2}$ and PEV were found to be 0.811, 0.816 and 2.01% for SRM model and 0.773, 0.777 and 3.5% for HEC-HMS, respectively. Sensitivity analysis of the models revealed that constant loss rate is very sensitive parameters for HEC-HMS model, whereas runoff coefficient is found to be most sensitive parameters for SRM model. In comparison between two models SRM model has given slightly better simulation results compared to HEC-HMS model.

• Spatio-temporal variations in precipitation on the Huang-Huai-Hai Plain from 1963 to 2012

Spatio-temporal variations in precipitation are affecting agricultural production in China in the context of climate change. Based on daily precipitation data from 63 national meteorological stations on the Huang-Huai-Hai Plain from 1963 to 2012, this paper analysed the spatio-temporal variations in precipitation in terms of precipitation days and intensity, using spatial interpolation, linear trend estimation and wavelet analysis. The results indicated that: (i) from 1963 to 2012, the number of annual precipitation days and intensity decreased gradually from the southeast to the northwest. Additionally, the distribution of the extreme precipitation index was similar to that of the annual precipitation index; (ii) the number of annual precipitation days and heavy precipitation days gradually decreased, while precipitation intensity and extreme precipitation days and extreme rainfall intensity remained relatively stable or decreased. The spatial patterns of annual variation trends were considerably different. The annual precipitation days and intensity trends are consistent with the overall trend, while that of the extreme rainfall index in some regions differs from the overall trend; (iii) the precipitation index displayed different periodic oscillations during the period, and the precipitation index values differed at different time scales. However, all the precipitation index values exhibited a 28-yr oscillation.

• Interaction between felsic granitoids and mafic dykes in Bundelkhand Craton: A field, petrographic and crystal size distribution study

In Bundelkhand Craton of central India, mafic dykes intruded when granitoids was partly crystallized. Cuspate–lobate boundary along the contact of granitoids and mafic magma indicates magma mingling in outcrop scale while textural evidence of mingling is represented by acicular apatite morphologies, titanite–plagioclase ocelli and ophitic–subophitic texture, mafic clots, resorbed plagioclase, and hornblende–zircon associations. Mingling also caused thermal exchange and fluid activity along the boundary between two coeval magmas. Crystal size distribution analyses for hornblende in the mafic rocks yield concave up curves which is also consistent with interaction of felsic and mafic magmas.

• Effect of uncertainty in $V_{\mathrm{S}}{-}N$ correlations on seismic site response analysis

This paper studies the reliability of the calculated shear-wave velocity $(V_{\mathrm{S}})$ from different available $V_{\mathrm{S}}$ and SPT-N correlations in terms of seismic site response analysis. In the present study, various $V_{\mathrm{S}}–N$ correlations developed for different regions around the globe have been used to calculate the bound of $V_{\mathrm{S}}$ variations with depth at three different sites in Kolkata city. This bound has later been used to generate the random $V_{\mathrm{S}}$ profiles using the Monte Carlo simulation. Equivalent linear site response analysis has been performed to study the response of those generated profiles under different input motion excitations. Strong-to-weak ground motion records have been used for this purpose. The amplification spectra of the generated $V_{\mathrm{S}}$ profiles using all soil types and specific soil-type $V_{\mathrm{S}}–N$ correlations show significant variations. The study also shows that the $V_{\mathrm{S}}–N$ correlation may result in quite different $V_{\mathrm{S},30}$ values and subsequently it may lead to the different site classes according to the NEHRP 2003 classification. So, the random choice of the $V_{\mathrm{S}}–N$ correlation, where the direct measurement of $V_{\mathrm{S}}$ is not available, may affect the outcome of seismic hazard analysis significantly. The study points out the need for accurate estimation of the $V_{\mathrm{S}}$ profile either from in-situ determination or using site-specific correlation.

• Geochemical assessment of fluoride enrichment and nitrate contamination in groundwater in hard-rock aquifer by using graphical and statistical methods

This systematic study was carried out with objective to delineate the various sources responsible for $\hbox {NO}_{3}^{-}$ contamination and $\hbox {F}^{-}$ enrichment by utilizing statistical and graphical methods. Since Central Ground Water Board, India, indicated susceptibility of $\hbox {NO}_{3}^{-}$ contamination and $\hbox {F}^{-}$ enrichment, in most of the groundwater, $\hbox {NO}_{3}^{-}$ and $\hbox {F}^{-}$ concentration primarily observed >45 and >1.5 mg/L, respectively, i.e., higher than the permissible limit for drinking water. Water Quality Index (WQI) indicates ${\sim }22.81\%$ groundwater are good-water, ${\sim }71.14\%$ groundwater poor-water, ${\sim }5.37\%$ very poor-water and 0.67% unsuitable for drinking purpose. Piper diagram indicates ${\sim }59.73\%$ groundwater hydrogeochemical facies are Ca–Mg–$\hbox {HCO}_{3}$ water-types, ${\sim }28.19\%$ Ca–Mg–$\hbox {SO}_{4}$–Cl water-types, ${\sim }8.72\%$ Na–K–$\hbox {SO}_{4}$–Cl water-types and 3.36% Na–K–$\hbox {HCO}_{3}$ water-types. This classification indicates dissolution and mixing are mainly controlling groundwater chemistry. Salinity diagram indicate ${\sim }44.30\%$ groundwater under in low sodium and medium salinity hazard, ${\sim }49.66\%$ groundwater fall under low sodium and high salinity hazard, ${\sim }3.36\%$ groundwater fall under very-high salinity hazard. Sodium adsorption ratio indicates ${\sim }97\%$ groundwater are in excellent condition for irrigation. The spatial distribution of $\hbox {NO}_{3}^{-}$ indicates significant contribution of fertilizer from agriculture lands. Fluoride enrichment occurs in groundwater through the dissolution of fluoride-rich minerals. By reducing the consumption of fertilizer and stress over groundwater, the water quality can be improved.

• # Journal of Earth System Science

Current Issue
Volume 128 | Issue 8
December 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019


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# Tent Spaces And Littlewood-Paley G-functions Associated With Bergman Spaces In The Unit Ball Of ℂn

Wei Ouyang, Zeqian Chen
Published 2011 · Mathematics
ABSTRACT In this paper, a family of holomorphic spaces of tent type in the unit ball of is introduced, which is closely related to maximal and area integral functions in terms of the Bergman metric. It is shown that these spaces coincide with Bergman spaces. Furthermore, Littlewood-Paley type g-functions for the Bergman spaces are introduced in terms of the radial derivative, the complex gradient and the invariant gradient. The corresponding characterizations for Bergman spaces are obtained as well. As an application, we obtain new maximal and area integral characterizations for Besov spaces.
This paper references

Some data provided by SemanticScholar


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# Charged particle multiplicities in pp interactions at $\sqrt {s} = 0.9$, 2.36, and 7 TeV

@article{Khachatryan2011ChargedPM,
title={Charged particle multiplicities in pp interactions at \$\sqrt \{s\} = 0.9 \$, 2.36, and 7 TeV},
}
• Measurements of primary charged hadron multiplicity distributions are presented for non-single-diffractive events in proton-proton collisions at centre-of-mass energies of $\sqrt {s} = 0.9$, 2.36, and 7 TeV, in five pseudorapidity ranges from |η| < 0.5 to |η| < 2.4. The data were collected with the minimum-bias trigger of the CMS experiment during the LHC commissioning runs in 2009 and the 7 TeV run in 2010. The multiplicity distribution at $\sqrt {s} = 0.9\;{\text{TeV}}$ is in agreement… CONTINUE READING


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# Animation Nodes: How can I rotate a Vector around a given Point

I was wondering how I could rotate a simple 3D Vector around a given point in 3d Space.

I am trying to rotate a simple position Vector (1,-2,1) around the world Center (0,0,0) on the Z Axis. If I rotate this vector around 180 degrees on the Z-Axis it should result in a new position vector (-1,2,1).

Geometry nodes is offering the Vector Rotate Node (https://docs.blender.org/manual/en/latest/render/shader_nodes/vector/vector_rotate.html?highlight=vector%20rotate)

Is there something similar in Animation Nodes? Or Any workaround?

Use Transform Vector node for doing any kind of transformation.


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#### Algebra & Combinatorics Seminar

##### Venue: LH-1, Mathematics Department

We will present some recent studies on ideals of the form $I_{1}(XY)$, where $X$ and $Y$ are matrices whose entries are polynomials of degree at most 1. We will discuss, how a good Groebner basis for these ideals help us compute primary decompositions and gather various other homological informations.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 14 Feb 2020


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# Two questions about counter example for Torelli theorem for hyperkahler manifolds

i am reading the article "Counter-example to global Torelli problem for irreducible symplectic manifolds" by Yoshinori Namikawa and i have two questions i can't answer:

1) he takes $T$ a complex torus, $Sym^3(T)$ the symmetric 3-product and $\alpha:Sym^3(T)\rightarrow T$ the sum map. Then he writes $K^2(T)$ for the generalized Kummer variety of dimension $4$, $\overline{K}^2(T)$ for $\alpha^{-1}(0)$ and $\sum$ for the singular locus of $\overline{K}^2(T)$. Of course $K^2(T)$ and $\overline{K}^2(T)$ are bimeromorphic and the exceptional locus is an irreducible divisor $E$ (which i believe is the irreducible divisor of $Hilb^3(T)\rightarrow Sym^3(T)$ intersected with $K^2(T)$). Finally, let $F$ be a resolution of $E$ and so there is a holomorphic surjective map from $F$ to $\sum$: Namikawa claims this is the Albanese map of $F$. For sure my knowledge about the Albanese map is very limited, but i can't see why this is the Albanese map of $F$.. could you give me a hint?

2) Given $T$ a complex torus and $T^*$ its dual, we know that there is a class $\delta\in H^2(K^2(T),\mathbb{Z})$ such that $H^2(K^2(T),\mathbb{Z})=H^2(T,\mathbb{Z})\oplus\mathbb{Z}\delta$, $H^{1,1}(K^2(T))=H^{1,1}(T)\oplus\mathbb{C}\delta$ and $2\delta=E$ where $E$ is the class of the exceptional divisor of $Hilb^3(T)\rightarrow Sym^3(T)$ intersected with $K^2(T)$. The class $\delta^*$ is the class in $H^2(K^2(T^*))$ with the same properties.

Namikawa takes $T$ complex torus with $NS(T)=0$ and dual torus $T^*$ not isomorphic to $T$. Then proves that if $f:K^2(T)--\rightarrow K^2(T^*)$ is a meromorphic map, then it is an isomorphism in codimension 1 and it must be $f^*(\delta^*)=\pm \delta$ (and i'm ok with that) but then says that "since $2\delta$ (resp. $2\delta^*$) is represented by $E$ (resp. $E^*$) the case $f^*(\delta^*)=- \delta$ does not occur because $K^2(T)$ and $K^2(T^*)$ are kahler manifolds". This sentence is what i'm not understanding: i don't know ho to use the kahler hypothesis and the fact that $2\delta =E$ to exclude $f^*(\delta^*)=- \delta$. Also, he wants to prove $f^*(\delta^*)= \delta$ because then $f$ induces a meromorphic map between $E$ and $E^*$, so i don't understand how the hypothesis $2\delta=E$ could be useful..

Thank you very much, i'm very sorry because i understand these are quite specific questions, but i would be very grateful to you if you could give me a hand because i'm out of ideas..

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Regarding (1),it looks to me like $\Sigma$ is the image of an embedding $T\to \overline{K}^2(T)$ sending $p$ to $2(\underline{-p}) + \underline{2p}$. Also, $F$ seems to be bimeromorphic to a projective space bundle over $\Sigma$. Since the Albanese variety is a bimeromorphic invariant, that would imply that the map from $F$ to $\Sigma$ is (equivalent to) the Albanese morphism for $F$. – Jason Starr Jul 3 '14 at 14:16
yes! thak you, i think you're right, because given the resolution of singularities $Hilb^3(T)\rightarrow Sym^3(T)$ we have that generally the fiber on the singular locus is a $\mathbb{P}^1$, so intersecting with $Ker(\alpha)$ we can say $F$ is bimeromorphic to a $\mathbb{P}^1$-bundle on $T$, which of course has $T$ as Albanese variety! – igor guedz Jul 3 '14 at 14:24

Question 1. It's not hard to see that $F$ is $\Sigma \times {\Bbb C} P^1$ and $\Sigma$ is a torus. Therefore the Albanese map is a projection to a torus.

Question 2. If $f^* \delta=-\delta$, then the effective cycle $f^* \delta+\delta$ is homologous to 0. On a Kahler manifold this is impossible, because an integral of a Kahler form over an effective cycle is always positive.

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24
April

## Free K-12 Workshops at UNR

Free NCLab STEM workshops for K-12 schools at UNR were introduced in February 2014 and they quickly became popular. Often we host three school trips per week. School buses come from Reno but also from towns as much as 130 miles away. If you are interested in exposing your students to introductory computer programming and 3D modeling (both are essential STEM skills), all you need to do is to fill and submit the form below.

## Register Now!

[contact-form-7 id="10094" title="NCLab Request - Free K-12 Workshop at UNR"]

## Logistics

NOTE: The capacity of our computer lab limits one workshop to 25 students. Minimum recommended age of students is 10-11 years (4-5th grade). Typical timing: Arrival at UNR between 9:30 and 10 am. Computer programming 90 - 120 minutes. Lunch 30 minutes. 3D modeling 60 - 90 minutes. Departure from UNR around 2 pm. Please keep in mind that for most school districts it takes at least 3 weeks to schedule a bus.

23
April

## Caughlin Ranch Elementary

On Monday we hosted a workshop for the gifted and talented program at the Caughlin Ranch Elementary School. These 3rd-graders were simply amazing!   Girls were the fastest learners as usual: Working on Karel games ignites collaboration and communication:

21
April

## Karel Course - New Edition

New edition of the Karel programming course just became available! It has stunning graphics, new games, and improved autograding. Visit course web page for more information.

## Request free evaluation copy!

Teachers can request free evaluation copy by filling a simple online form.

While improving the NCLab's self-paced 3D Modeling course, we decided to change the order of arguments in the ROTATE (R) command in PLaSM. This change is not backward compatible but adjustments are easy to make. Previously, the order of the arguments was:  R(object, axis, angle)  After the change, the last two are switched:  R(object, angle, axis)  What is the advantage? The new format allows users to skip the axis in 2D where it is irrelevant (rotation always is about the z-axis in 2D):  R(object, angle)  If the axis is left out in 3D, then the z-axis is used by default as well. The extension from 2D to 3D is now more natural. The 3D modeling textbook, all course projects and solutions, examples, demo scripts, and help documents have been updated. We are moving on!


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# Full-rank factorization of the graph Laplacian

Is there a combinatorially meaningful full-rank factorization of the Laplacian matrix of a graph?

The usual factorization $L=BB^{T}$, where $B$ is an oriented incidence matrix, is full-rank if and only if the graph is a tree (because then $B$ has $n-1$ columns and rank $n-1$). Is there a nice way to to factorize a connected graph with cycles?


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All these are the polymers of glucose. Cytosine is a pyrimidine base found in DNA monomers. Block copolymer—Polymer made of two or more monomer species and identical monomer units (“mers”) occurring in relatively long sequences along the main polymer chain. They are unbranched chains of amino acids. We assume that our polymers are swollen since they are immersed in a good solvent (\chi 1/2 Another factor that differentiates cellulose from other polysaccharides is its reaction with the iodine solution. Thymine is the one nitrogen base found in DNA but not in ribonucleic acid, or RNA. In present work, a coarse-grained model of the planar polymer brushes consisting of polymer chains pinned by one end to a ﬂat impenetrable surface was used. Upon complete hydrolysis, starch yields glucose molecules. E.g. The unit which repeats itself in the polymer is called REPEATING UNITS. Polymers are the macromolecules formed when several identical repeating units combine to form long chains as a result of chemical bonding. Their consequently large molecular mass relative to small molecule compounds produces unique physical properties, including toughness, viscoelasticity, and a tendency to form glasses and semicrystalline structures rather than crystals. Chains form when the same basic unit is repeated over and over. However, large stores of glycogen are found in liver and muscle cells. Polymers, both natural and synthetic, are created via polymerization of many small molecules, known as monomers. Imagine a long polymer, made of N rod-like units, each of length l, attached end-to-end. Polymer. Deoxyribonucleic acid (DNA), the genetic “blueprint” for all known life, encodes the information for all the other molecules that make up an organism, and it is DNA that carries inherited traits from one generation to the next. HOMOPOLYMER Homopolymers are synthesized from a single type of monomer . Polymers are long chained molecules formed by joining up many identical repeating sub-units called monomers. Depending on the nature of amino acids, they may or may not be soluble in water. Polymers are identified based on their properties. The process in which relatively small molecules, called monomers, combine chemically to produce a very large chainlike or network molecule, called a polymer, is named Polymerization. Monomer: A molecule that can be bonded to other identical molecules to form a polymer Dimer: MS/MS analysis. DNA consists of paired polymers made up of four different monomers. where M represents the monomer and n is a very big integer These chains then undergo different structural arrangements resulting in the formation of functional proteins. A chemical reaction forming polymers from monomers is called polymerization, of which there are many types. If there is more than one type of unit, this is known as a co-polymer. It is the most abundant carbohydrate present in nature. A polymer that consists entirely of one type of monomer unit is called a homopolymer. It is also sometimes called animal starch. If the diad consists of units oriented in opposition, the diad is called a racemo diad … Synthetic rubber, used for various purposes. A polymer is a large molecule a. made up of long chains of atoms held together by hydrogen bonds b. made up of long chains of atoms covalently bonded together c. made up of a large lattice structure held together by ionic bonds d. always made up of identical monomer units Polymers make up many of the materials in living organisms, including, for example, proteins, cellulose, and nucleic acids. A monomer unit is refers to a monomer as a building block in a compund. Glycogen gives red color with Iodine. It may consist of branched chains of glucose as in amylopectin starch, or unbranched chains of glucose as in amylose starch. Both glycogen and starch are digestible in the human intestinal tract. Proteins are a commonly f… 2. By Monomer Homo Polymers A polymer consist of identical monomers is called homo polymer. In the Greek language, polymer literally means “many parts.” Polymers are being used more and more in medical devices, such as drug delivery, screws, plates, fixation pins, … Polypeptides are the polymers of amino acids. Take the following examples; 1. The monomer "in place" in a polymer is called a repetitive group. They are present within the bodies of living organisms and carry out essential life processes. Polymers make up many of the materials in living organisms, including, for example, proteins, cellulose, and nucleic acids. They are also single unbranched chains consisting of 13 or more nucleotides. A homopolymer has repeating units of the same monomer, such as polyvinylchloride. By Monomer Homo Polymers A polymer consist of identical monomers is called homo polymer. Polypeptides from proteins that function as enzymes. A polymer can be a homopolymer or a heteropolymer. e.g. Disordered, in which the polymer has a somewhat amorphous or glassy structure. A polymer which contains only a single type of repeat unit is known as a homopolymer, while a polymer containing two or more types of repeat units is known as a copolymer. The nucleotides in RNA are also linked together via the phosphodiester bonds. This enzyme is also present in the human digestive tract that digests the nucleic acid taken in the form of diet into nucleotides that can be absorbed. The physical properties of a polymer are highly dependent on its morphology which in turn is dependent on the interaction between the chains of monomers present in it. It is made up of branched chains of glucose that are arranged in the form of a helix. However, those methods are beyond the scope of our subject. Unraveling a pathway to menopausal bone loss. Polymerisation is a process by which the monomers are joining together into chain-like big molecules known as polymers. This usually implies that the polymer is made from all identical monomer molecules . It must be made up of identical repeating units called monomers. Polymers form an important part of our system, as mentioned above. Cellulose is a branched polymer of glucose subunits that are linked via glycosidic bonds. Natural rubber (see above Natural occurrence) is a polymer of 2-methyl-1,3-butadiene (commonly called isoprene). Polypeptides are the polymers made up of single, unbranched chain of amino acids linked via peptide bonds. These polypeptides undergo different spatial organization to form complex structural and functional proteins. Cross-linked, in which the chains of monomers show extensive cross-linking. A repeat unit is sometimes called a mer or mer unit. 2. a long chain molecule made up of many small identical units called monomers. the smallest repeating unit of a polymer. Monomers can have linear or branched configuration. Modern naming of polymers is to put the name of the monomer in brackets after the word poly. Each monomer unit is identical and is repeated dozens to millions of times. NAD can restore mitochondrial function and energy…, Long noncoding RNA identified as a key regulator of…, RNAs play key role in protein aggregation and in…, Parental 'feeding styles' reflect children's genes, Researchers map previously unknown disease in children, Tiny molecule has big effect in childhood brain…, Researchers find inhibiting one protein destroys…, Testosterone therapy in hypogonadism can prevent…, Type 2 diabetes screening in community pharmacies could increase early diagnosis, Hormone therapy helps strengthen brain connections in transgender women, How does estrogen protect bones? Starch, glycogen, and cellulose are the most important polysaccharide. The common properties that are found in all types of polymers are as follows; 1. Main Difference – Homopolymer vs Heteropolymer. Our definitions. While many people use the term 'polymer' and 'plastic' interchangeably, polymers are a much larger class of molecules which includes plastics, plus many other materials, such as cellulose, amber, and natural rubber. A molecule from which a polymer is made is called a monomer. Here ethylene (ethene) is the monomer, and the corresponding linear polymer is called high-density polyethylene (HDPE). Artificial polymers: They are artificially made in industries for various commercial uses. An oligomer is also a type of polymer. Each vinyl chloride monomer molecule contributes a CH 2 group joined to a CHCl unit by a single bond. Polymers form an important part of our system, as mentioned above. Monomers in each polymer have a particular configuration or arrangement that is a specific characteristic of that polymer. Polymers are the macromolecules formed by the combination of many small monomers. It can also be identified by using the iodine test. However, it is not present in animal cells. Following properties are common in all polysaccharides: Some biologically important polysaccharides include Starch, Glycogen, and Cellulose. That is why cellulose is not digestible by the human digestive system. Neuropeptides in the human body act as neurotransmitters. The word polymer comes from poly-(many) and -mer (part). Polymers are macromolecules that are made out of small basic units called monomers. Assume that the connections between the monomers are completely flexible so that the rods can make any angle with respect to one another. They are critical components of any bubble juice and can provide a number of important qualities. The repeating structural unit of most simple polymers not only reflects the monomer(s) from which the polymers are constructed, but also provides a concise means for drawing structures to represent these macromolecules. Thus, the functions performed by polypeptides in the human body are the same as performed by proteins. Polymers are identified based on their properties. The method by which polymers are made artificially in the industry is known as polymerization. Polypeptide is made up o… 6 7. Oligomer. poly(e thene), poly(chloroethene). A monomer ( MON-ə-mər; mono-, "one" + -mer, "part") is a molecule that "can undergo polymerization thereby contributing constitutional units to the essential structure of a macromolecule". Thymine is the second pyrimidine base found in DNA and it forms bonds with adenine on the second DNA strand. A polymer is a large molecule that is made from many small repeating chemicals called monomers. DNA undergoes degradation by nucleases that cleave the phosphodiester bond between nucleotides. Signup as a free member below and you'll be brought back to this page to try the sample materials before you buy. The polymer made up with repetition of similar type of polymer is called ‘homo-polymer’. These include the following; These polymers of amino acids have several other functions that will be discussed somewhere else in detail. They can also be attached to a lipid molecule to form a lipopeptides. Dimers, trimers, and tetramers are, for instance, oligomers composed of two, three, and four monomers, respectively. It’s made of two carbon atoms, three hydrogens and one chlorine atom. Copolymer (two or more types of monomers). Polymer - a long chain molecule made up of many small identical units of Monomer is known as Polymer. Large quantities of monomers combine to form polymers in a method called polymerization. The word polymer means many parts (“poly” = many and “mer” = parts); this term originated from two Greek words “polus” (= many) and “meros” (= parts). It can also be used to confirm the target A molecule or molecular complex consisting compound has been made if the reaction pathway is well of two identical molecules linked together Trimer: A polymer comprised of three monomer units Contrary to the DNA, it consists of only a single long chain of nucleotides. The word polymer is derived from two Greek words; ‘poly’ meaning ‘many’, and ‘mer’ meaning ‘part’. HDPE is composed of macromolecules in which n ranges from 10,000 to … Video: Nighttime Skincare Routine | Anti Aging for over 35 skin! Linear, in which all the monomers are arranged in a single chain. A compound must have the following properties to be a polymer; Two broad categories of polymers include; Depending on the nature of monomers forming a polymer, they are classified as; Artificial polymers made for industrial and commercial uses include artificial rubber, PVC, nylon, etc. Polymer nomenclature is generally based upon the type of monomer residues comprising the polymer. I use shopping trolleys to represent monomers, then when they are pushed together in … It is the base ring that differentiates the four otherwise identical monomers; they get their names from their respective nitrogen bases. Synthetic Polymers Polymers synthesized in laboratory from low molecular weight compounds, are called as, synthetic polymers. An oligomer ( (listen)) (oligo-, "a few" + -mer, "parts") is a molecular complex of chemicals that consists of a few monomer units, in contrast to a polymer, where the number of monomers is, in principle, infinite. The polymer made can either be made up of the similar single unit (monomers) or different types of single units can get combine to form usually a chain like structure called polymer. Morphology indicates the final shape of the polymer it assumes after the process of polymerization. Most polymers are carbon based, with various other elements (hydrogen, oxygen, nitrogen being common ones) placed strategically. A polymer needs to be made up of identical repeating units. Starch always yields blue color in the iodine test. If the diad consists of two identically oriented units, the diad is called a meso diad reflecting similar features as a meso compound. A polysaccharide is a polymer made up of several repeating monosaccharide. It can be identified by iodine test. Her work has been featured in "Kaplan AP Biology" and "The Internet for Cellular and Molecular Biologists." E.g. Starch is the main form in which the glucose is stored in plants. Few examples of artificial or synthetic polymers include: These polymers are made in industry by the process of polymerization. Proteins are a commonly f… Adenine is one of the two purine bases found in DNA monomers. Guanine monomers form base pairs with cytosine monomers on the other DNA strand. It is also present in chloroplast of animal cells as well as mitochondria of both animal and plant cells. Deoxyribonucleic acid (DNA) is a polymer of deoxyribonucleotides. A polysaccharide is a polymer made up of several repeating monosaccharide. In this case, monomers have two configurations. Deoxyribonucleic acid (DNA), the genetic “blueprint” for all known life, encodes the information for all the other molecules that make up an organism, and it is DNA that carries inherited traits from one generation to the next. Monomer - the smallest repeating unit is known as Monomer. In the case of synthetic polymers, it is easier to find the chain length as the statistical data is being reported during the process of polymerization. "Mer" originates from the Greek word "meros," which means a part. A polymer is composed of repeating monomer units and can either be natural or synthetic. The common properties that are found in all types of polymers are as follows; 1. A terpolymer is a copolymer which contains three types of repeat units. All the structural and functional information of a cell is stored in the form of DNA. The monomers consist of a deoxyribose sugar molecule, a phosphate group and a nitrogen base ring. It is a double polymer i.e. Biological polymers are large molecules composed of many similar smaller molecules linked together in a chain-like fashion. The commonly used reactive monomers for free radical photopolymerizations are acrylates and methacrylates. Block: two or more different homopolymers are bonded together, for example, …AAAABBBB… 4. If all units are identical, the polymer is named homopolymer, if the monomer units are dierent, the polymer is named heteropolymer. They are present in hair, nails, bones, and cartilage, etc. Alternating: two different units alternate with one another, for example, …ABABAB… 2. Polypeptide is made up o… Polyethylene, PVC, Polypropylene, Nylon 6 Co Polymers A polymer consist of monomers of different chemical structure are called copolymers. In a branched polymer, some monomers form short chains that are attached as a branch to the main linear chain of monomers. A polymer can be a homopolymer or a heteropolymer. Polymerisation can be represented graphically as shown below. Often made with pigments and fillers for color and strength. RNA taken in diet is digested by nuclease of the digestive tract into nucleotides that are then absorbed into the blood. In RNA, thymine is replaced by uracil, another pyrimidine that can also form bonds with adenine. Carbohydrates,Protein s,Nucleic acids - are chain like molecules called Polymer. Take the following examples; 1. webew7 and 7 more users found this answer helpful. In this process, monomers are combined forming covalent bonds or linkages. This information is also passed onto the next generation via DNA. Unit-25 - POLYMER IMPORTANT POINTS § INTRODUCTION Polymer : Polymer (poly = many ; meros = parts) : is defined a material which is made by linking together a large number of small recurring units called monomers. 476 views If different types of molecules are joined together to form a larger molecule, it is simply called a giant molecule, not a polymer. This single bond is a remnant of the double bond which joined those groups in the vinyl chloride molecule. multiple chains of monomers can be combined at one time to form a polymer. Is a long molecule consisting of many similar or identical building block linked by covalent bonds. Polystyrene, polyacrylonitrile, polyethylene, and many more. Following properties are shared by all polypeptides; Polypeptides undergo different structural arrangements to form proteins. Polymer, any of a class of natural or synthetic substances composed of very large molecules, called macromolecules, that are multiples of simpler chemical units called monomers. Coordination polymerization conditions have been developed that convert isoprene to a polymer with properties identical to that of natural rubber. The process through which monomers from polymer is called polymerization. Rest of our discussion will be based on these bio-polymers. Several thousands of monosaccharide subunits combine via glycosidic bonds to form polysaccharides. This is just what happens in an addition reaction of an alkene. It is a polymer of ribonucleotides. Polymers can also be classified based on the type of monomers present in them. When making bubble juice, it is often convenient to use easily found household products (such as KY Jelly Personal Lub… No problem. (carbohydrate) A polymer made of many saccharide units linked by glycosidic bonds. As with adenine, a guanine-containing monomer will contain a guanine ring bonded to the 1′ carbon atom of deoxyribose with a phosphate group bound to the 5′ carbon of the sugar. A polymer may be a natural or synthetic macromolecule comprised of repeating units of a smaller molecule (monomers). A polymer is composed of repeating monomer units and can either be natural or synthetic. There are natural and synthetic oligomers and polymers. A heteropolymer has two or more different monomer units. Wellknown monomers are: vinyl chloride H2C=CHCl ... nucleotides which are made of deoxyribose, a nitrogenos base, and … The only difference in structure between thymine and uracil is that thymine contains a methyl group or a carbon and three hydrogen atoms, bonded to the 5′ carbon atom. A material consisting of such polymer molecules. (ESCM5) Polymers are large molecules (macromolecules) that are made up of many repeating structural units called monomers which have various functional groups. The size of the polymer depends on its chain length. The building blocks of a polymer are called monomers.The process of producing a polymer through a monomer is called polymerization.Some polymers are made of the same type of monomers. They are often used in dishwashing liquid and shampoos and food stuffs to provide viscosity. A polynucleotide is a single chain containing 13 or more nucleotides attached via phosphodiester bonds. In this section, we will have a detailed discussion on polymers, their characteristics and properties, their classification, examples and much more. The individual smaller molecules are called monomers.When small organic molecules are joined together, they can form giant molecules or polymers. We all use different synthetic polymers in our daily lives. Upon proteolysis, they yield different amino acids. Following morphologies of polymer are usually seen; They are classified into two broad categories. Polyvinyl Chloride (PVC), used in plastic and pipe industry. Some polymers are natural and made by organisms. These glycosidic bonds are different from those in starch and glycogen in a way that they cannot be broken in the human body. This shows how the chemical composition of a polymer consists of many smaller units (monomers) bonded together into a larger molecule. These lipopeptides are the components of cell membranes and perform several functions essential for the growth and survival of the cell. A molecule from which a polymer is made is called a monomer. (chemistry) A long or larger molecule consisting of a chain or network of many repeating units, formed by chemically bonding together many identical or similar small molecules called monomers. A polymer is formed by polymerization, the joining of many monomer molecules. They can be natural or synthetic. Two adjacent structural units in a polymer molecule constitute a diad. The basic structural unit, repetition of which gives the polymer is called “monomer”. For polyethylene, arguably the simplest polymer, this is demonstrated by the following equation. In short: we provide absolutely everything you need to pass A-Level Biology: International Union of Pure and Applied Chemistry. These are the polymers made by repeating units of monosaccharides. Most polymers are still known by their original names or trade names. Take the following examples; The configuration of monomers is the second property of polymers. Polymer is a term used to describe large molecules consisting of repeating structural units (monomers) connected by covalent chemical bonds. Glycogen is also a polymer of glucose molecules and yield glucose on complete hydrolysis. Nice clear polymer with a nice shine. Copolymer – a polymer made from more than one kind of monomer. Monomer If you want to see what we offer before purchasing, we have a free membership with sample revision materials. 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text:
D. Journey
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Stewie the Rabbit explores a new parallel universe. This two dimensional universe has the shape of a rectangular grid, containing n lines and m columns. The universe is very small: one cell of the grid can only contain one particle. Each particle in this universe is either static or dynamic. Each static particle always remains in one and the same position. Due to unintelligible gravitation laws no two static particles in the parallel universe can be present in one column or row, and they also can't be present in the diagonally adjacent cells. A dynamic particle appears in a random empty cell, randomly chooses the destination cell (destination cell may coincide with the start cell, see the samples) and moves there along the shortest path through the cells, unoccupied by the static particles. All empty cells have the same probability of being selected as the beginning or end of the path. Having reached the destination cell, the particle disappears. Only one dynamic particle can exist at one moment of time. This particle can move from a cell to a cell if they have an adjacent side, and this transition takes exactly one galactic second. Stewie got interested in what is the average lifespan of one particle in the given universe.

Input

The first line contains two space-separated integers: n, m (2 ≤ n, m ≤ 1000) which represent the sizes of the universe. The next n lines containing m symbols each describe the universe without dynamic particles — the j-th symbol of the i-th line equals to 'X' if the cell is occupied by a static particle, and to '.' if it is empty. It is guaranteed that the described universe satisfies the properties described above, that is no two static particles can be in one column or in one row, besides, they can't be positioned in the diagonally adjacent cells.

Output

You have to print on a single line a single number which is the average life span of a particle with an accuracy of at least 6 decimal places.

The answer will be accepted if it is within 10 - 6 of absolute or relative error from the correct answer.

Examples
Input
2 2...X
Output
0.888888888889
Input
3 3....X....
Output
2.000000000000