Abstract:
A few properties of unitary Cayley graphs are explored using their eigenvalues. It is shown that the adjacency algebra of a unitary Cayley graph is a coherent algebra. Finally, a class of unitary Cayley graphs that are distance regular are also obtained. Key Words: Adjacency Algebra, Circulant Graph, Coherent Algebra, Distance Regular Graph,Ramanujan's sum . AMS(2010): 05C25, 05C50

Abstract:
Let $n$ be an even positive integer with at most three distinct prime factors and let $\ze_n$ be a primitive $n$-th root of unity. In this study, we made an attempt to find the lowest-degree $0,1$-polynomial $f(x) \in \Q[x]$ having at least three terms such that $f(\ze_n)$ is a minimal vanishing sum of the $n$-th roots of unity.

Abstract:
A single RP-HPLC method is developed for estimation
of isomeric impurities of vitamin D_{3} analogue-Calcipotriol/Calcipotriene
(Calci) and impurities of Betamethasone dipropionate (BD). The developed method is capable of separating impurities of Calci and
BD, specifically pre-Calcipotriene (Pre-Calci) from other known and unknown impurities.
Pre-Calci is isolated and is characterised using few analytical techniques.
These impurities are separated using a RP-C_{18} 150 × 4.6 mm, 2.7 μm column maintained at 50°C. The mobile phase consisted of mixture of water,
methanol, acetonitrile and tetrahydrofuran eluted in gradient mode. Detection
was done at 264 nm and 240 nm for Calci and BD impurities respectively. The
method can be used for determining quality of Calci and BD drugs and ointment
based drug products. It is stability indicating related substance method for
both the drugs and drug products.

Abstract:
We give necessary and sufficient conditions for a few classes of known circulant graphs and/or digraphs to be singular. The above graph classes are generalized to $(r,s,t)$-digraphs for non-negative integers $r,s$ and $t$, and the digraph $C_n^{i,j,k,l}$, with certain restrictions. We also obtain a necessary and sufficient condition for the digraphs $C_n^{i,j,k,l}$ to be singular. Some necessary conditions are given under which the $(r,s,t)$-digraphs are singular.

Abstract:
A graph $X$ is said to be a pattern polynomial graph if its adjacency algebra is a coherent algebra. In this study we will find a necessary and sufficient condition for a graph to be a pattern polynomial graph. Some of the properties of the graphs which are polynomials in the pattern polynomial graph have been studied. We also identify known graph classes which are pattern polynomial graphs.

Abstract:
Let $\K$ be a finite extension of a characteristic zero field $\F$. We say that the pair of $n\times n$ matrices $(A,B)$ over $\F$ represents $\K$ if $\K \cong \F[A]/< B >$ where $\F[A]$ denotes the smallest subalgebra of $M_n(\F)$ containing $A$ and $< B >$ is an ideal in $\F[A]$ generated by $B$. In particular, $A$ is said to represent the field $\K$ if there exists an irreducible polynomial $q(x)\in \F[x]$ which divides the minimal polynomial of $A$ and $\K \cong \F[A]/< q(A) >$. In this paper, we identify the smallest circulant-matrix representation for any subfield of a cyclotomic field. Furthermore, if $p$ is any prime and $\K$ is a subfield of the $p$-th cyclotomic field, then we obtain a zero-one circulant matrix $A$ of size $p\times p$ such that $(A,\J)$ represents $\K$, where $\J$ is the matrix with all entries 1. In case, the integer $n$ has at most two distinct prime factors, we find the smallest 0-1 companion-matrix that represents the $n$-th cyclotomic field. We also find bounds on the size of such companion matrices when $n$ has more than two prime factors.

Abstract:
In view of the importance of picolinic acid (Pa) in preventing cell growth and arresting cell cycle, attempts were made to design, synthesize and characterize two new Pa based tetradentate ligands (DPPTR and DPPTY) with a modified procedure. The procedure reported here avoids by-products and provides better yield and purity.

Abstract:
A simple and sensitive
fluorescence detection of domperidone by ultra fast liquid chromatographic method
was developed and validated in human serum. For the evaluation of new drug delivery
systems, conducting of pharmacokinetic studies in human volunteers is essential
for approval to marketing after preclinical evaluation in animal models. The present
method consists of protein precipitation, extraction of analytes from human serum
into dichloromethane and separation using reversed-phase C_{18} column.
Propranolol hydrochloride was used as an internal standard and the eluent was monitored
by fluorescence detector at excitation 282 and emission 328 nm. The mobile phase
used was 62:38 ratio of 10 mM phosphate buffer pH adjusted to 3.1 with OPA and methanol
at a flow rate of 1 mL·min^{-1}. The method was evaluated for assay, LLOD, LLOQ, recovery
and stability studies. The retention times for domperidone and propranolol hydrochloride
were found to be 6.36 and 7.94 minutes respectively. The intraday and inter-day
coefficient of variation and percent error values of assay method were less than
5%; mean recovery was more than 96% for each analyte and the method was found to
be precise, accurate and specific during study. The method was successfully applied
for pharmacokinetic study of immediate and controlled release bioadhesive hot melt
extruded buccal patches of domperidone after buccal administration to healthy human
volunteers. The C_{max}, T_{max}, and AUC_{0–24 }of domperidone
from immediate and controlled release buccal patches were found to be 129.7 ng·mL^{-1}, 1.5 h, 455.1 ng·h·mL^{-1} and 145.7 ng·mL^{-1}, 5.25
h, 911.0 ng·h·mL^{-1} respectively. A simple, sensitive and reliable method for
the fluorescence determination of domperidone in human serum by UFLC method was
developed and validated.

Abstract:
Textile manufacturing units involved in finishing processes are profuse water consumers. The effluents from these plants are major source of water pollution. Poly Aluminium Chloride (AlCl3 6H2O) is used as a coagulant for the removal of Chemical Oxygen Demand (COD) of selective reactive dyes, which are used for cotton yarn dyeing, at different doses. The results indicate that the removal of COD of various dyes RB41, RB209, RB204 and RB184 are 68, 40, 36, and 29 percent respectively at their optimum doses. The optimum doses of Poly Aluminium Chloride (PAC) for RB41, RB209, RB204 and RB 184 are 5.2, 34.3, 20 and 22mg of PAC per mg. of COD removed, respectively.

Abstract:
Lipid abnormalities are major risk factors for premature coronary artery diseases. We investigated serum lipids andthe prevalence of dyslipidemia in urban adult population in Warangal district of Andhra Pradesh. We studied 1496individuals 20–90 years of age. Health status was determined by questionnaires and physical check-ups. Totalcholesterol (TC), LDL-cholesterol (LDL-C), HDL-cholesterol (HDL-C) and total triglycerides (TGs) were measured. TC>5.7 mmol/L, LDL-C >3.6 mmol/L, TGs >1.7 mmol/L, and HDL-C <0.9 mmol/L were defined as abnormal. Meanserum TC, LDL-C, and TG concentrations were increased. 52.7% of males and 42.9% of females having at least oneabnormal lipid concentration. HDL-C was abnormally low in 7% of males and in 1.6% of females. The prevalence ofhypercholesterolemia, hypertriglyceridemia and abnormally low HDL-C, especially the presence of slighthypertriglyceridemia, were higher in all age groups. The increase was most prominent in the middle age group (40–59 years). Hypercholesterolemia, hypertriglyceridemia and abnormally low HDL-C have increased considerably overthe past 10 years in urban adult populations in Warangal district, Andhra Pradesh. Dietary changes and less physicalactivity resulting from rapid improvements in living conditions may be the causes for the increases. Enhancedpreventive measures should be undertaken to modify these situations.