Codes and Orbit Covers of Finite Abelian Groups

It is well known that the discrete analogue of a lattice is a linear code which is a vector subspace of Hamming space $\mathbb{F}^n$. The set $\mathbb{F}$ is a finite field and $n \in \mathbb{Z}_{>0}$. Our attempt is to construct a class of lattices such that its discrete analogues are variable length non-linear codes. Let $\mathcal{G}$ and $\mathcal{H}$ be two finite groups, and let $\mathcal{S}$ be a fixed set of generators for $\mathcal{G}$. The homomorphism code is defined as the set of all homomorphisms from $\mathcal{G}$ to $\mathcal{H}$, denoted by, $\mathcal{C} = Hom(\mathcal{G}, \mathcal{H})$. To each homomorphism $\varphi$ between $\mathcal{G}$ and $\mathcal{H}$, a codeword $c_\varphi$ is associated, it is a vector of values of $\varphi$ on the generators in $\mathcal{S}$, that is, $c_\varphi = (\varphi(s_1), \varphi(s_2), \dots, \varphi(s_k))$, where $\varphi(s_i)$ is the image of $s_i \in \mathcal{S}$, $1 \leq i \leq k$. We provide a design to construct a variable length binary non-linear code called as automorphism orbit code from a finite abelian $p$-group of rank more than 1, where $p$ is a prime number. For each finite abelian $p$-group, the codewords of the automorphism orbit code are variable length codewords called as automorphism orbit codewords. Note that homomorphism codes are determined by homomorphisms between groups, whereas automorphism orbit codes are specified by partitions of a number, orbits of a group action, homomorphisms and automorphisms of groups. We make use of elements of $Hom(\mathcal{G}, \mathcal{H})$ to present a cover relation for bit strings of codewords of an automorphism orbit code and formulate a lattice of variable length non-linear codes. Finally, we discuss some information related to the future research work on connections to representation theory of groups and algebras

Correlation Estimates of Some Performance Traits of Thari Cattle

The studies were carried out during the year of May 2014 to May 2015 to estimate the correlation among some performance traits of Thari cattle. The recorded data which include three sires with 15 daughters from each sire and four lactations of each daughters were observed. The averaged birth weight and weaning of three sires daughters was found 17.7 + 1.75, 17.38 + 1.01, 17.4 + 1.92 and 43.18 + 2.07, 42.6 + 2.49, 42.7 + 4.19, respectively. The result showed that higher birth weight was observed in daughters of sire- B whereas the lowest birth weight was found in daughters of sire- C and the higher weaning weight was found in daughters of sire- A and lowest weaning weight was found in daughters of sire-B. The milk yield of 1st, 2nd, 3rd and 4th lactation yield of all daughter were found averaged 861.60±70.40, 1046.78 ± 62.36, 1200.91 ± 111.21 and 1070.87 ± 54.56 liters, respectively. The result showed that 3rd lactation yield was significantly (P<0.05) higher than 1st, 2nd and 4th. The sire wise birth weight, weaning, milk yield and lactation length showed a non-significant different. The results of simple correlation for birth weight x weaning weight and milk yield x lactation length were 0.478 and 0.548. The result of environmental correlation for birth weight x weaning weight and milk yield x lactation length were 0.05 and 0.91. The results of genetic correlation for birth weight x weaning weight and milk yield x lactation length were -0.008 and -0.67. The results of phenotypic correlation for birth weight x weaning weight and milk yield x lactation length were 0.06 and 0.24, respectively. Keywords: Genetic, Phenotypic, Environmental, correlation, Milk yield. Lactation Length, Birth weight, weaning weight

On the expansion constant and distance constrained colourings of hypergraphs

For any two non-negative integers h and k, h > k, an L(h, k)-colouring of a graph G is a colouring of vertices such that adjacent vertices admit colours that at least differ by h and vertices that are two distances apart admit colours that at least differ by k. The smallest positive integer {\delta} such that G permits an L(h, k)-colouring with maximum colour {\delta} is known as the L(h, k)-chromatic number (L(h, k)-colouring number) denoted by {\lambda}_{h,k}(G). In this paper, we discuss some interesting invariants in hypergraphs. In fact, we study the relation between the spectral gap and L(2, 1)-chromatic number of hypergraphs. We derive some inequalities which relates L(2, 1)-chromatic number of a k-regular simple graph to its spectral gap and expansion constant. The upper bound of L(h, k)-chromatic number in terms of various hypergraph invariants such as strong chromatic number, strong independent number and maximum degree is obtained. We determine the sharp upper bound for L(2, 1)-chromatic number of hypertrees in terms of its maximum degree. Finally, we conclude this paper with a discussion on L(2, 1)-colouring in cartesian product of some classes of hypergraphs

Some invariants related to threshold and chain graphs

Let G = (V, E) be a finite simple connected graph. We say a graph G realizes a code of the type 0^s_1 1^t_1 0^s_2 1^t_2 ... 0^s_k1^t_k if and only if G can obtained from the code by some rule. Some classes of graphs such as threshold and chain graphs realizes a code of the above mentioned type. In this paper, we develop some computationally feasible methods to determine some interesting graph theoretical invariants. We present an efficient algorithm to determine the metric dimension of threshold and chain graphs. We compute threshold dimension and restricted threshold dimension of threshold graphs. We discuss L(2, 1)-coloring of threshold and chain graphs. In fact, for every threshold graph G, we establish a formula by which we can obtain the {\lambda}-chromatic number of G. Finally, we provide an algorithm to compute the {\lambda}-chromatic number of chain graphs

GIS-Based Geotechnical Database for Collaborative GIS

INDOT spends at least 8 million dollars annually on geotechnical site investigations, not including the amounts spent by contractors. The laborious and costly job of data collection in geotechnical practice requires the efficient storing and organizing of this valuable data to develop correlations and trends in spatially varying geotechnical data. INDOT currently uses gINT software for managing geotechnical data and ArcGIS for storing boring logs and geotechnical reports. The INDOT geotechnical office is pursuing means to improve the efficiency of their operations by developing a GIS-based geotechnical database for secure storage, easy retrieval, and flexible sharing of geotechnical data to enhance decision making. SPR-4616 is the first step towards the development of a geotechnical data management system in which important decisions on the components and structure of the database were made. The report presents a detailed conceptual layout for the development of a geotechnical database following an object-oriented programming approach. The report discusses in detail the geotechnical applications, the field, laboratory, and verification tests that will be included in the database. The geotechnical variables required to perform the engineering analysis in designing specific applications are logically linked with the geotechnical tests from which they are obtained. Lastly, a detailed layout of the proposed database structure and a user workflow example is provided in the report and can serve as a guide during the development of the database system

Implementation Study: Continuous, Wireless Data Collection and Monitoring of the Sagamore Parkway Bridge

This report presents, in detail, the development and implementation of a wireless solar powered DAQ system for continuous real-time monitoring of the Sagamore Parkway Bridge using the data collected from strain gauges installed in the bridge pier and its foundation piles. The data analysis showed that there is no significant change in the load-settlement response of the bridge pier 3 years after its construction. The pile cap contribution in carrying the total load carried by the bridge pier is significant (about 20%). The hourly ambient temperature trends match with the incremental bending moments measured on the bridge pier and the piles. The daily temperature cycles also affected the load transferred between the piles within the pile group. The water level fluctuations of the Wabash River impacted the total load carried by the pier, such that a rise in water level resulted in slight drop in the total load carried by the bridge pier due to buoyant forces. The overall results of the bridge monitoring showed that the bridge has performed well since its construction

Tropical diabetic hand syndrome- a case report with a short review

Tropical diabetic hand syndrome (TDHS) encompasses an acute symptom complex found in patients of diabetes mellitus primarily in the tropical regions. The syndrome usually follows a minor trauma to the hand, may rapidly progress to gangrene, fulminant sepsis and may even be life threatening. The syndrome is less recognized and thus reported less often. The authors present here a case of Tropical diabetic hand syndrome (TDHS) in a middle aged female with a poor glycemic control. The patient was managed meticulously both by surgical debridement and proper, culture evidenced antibiotic therapy apart from routine diabetic management