# Papers

Bijendra Singh
School of studies in Mathematics, Vikram University, Ujjain M.P. (INDIA)
Rachana Khandelwal
School of studies in Mathematics, Vikram University, Ujjain M.P. (INDIA)
Nitu Trivedi
School of studies in Mathematics, Vikram University, Ujjain M.P. (INDIA)

ABSTRACT:

A prey-predator SIS model with logistic growth has been considered with parasitic infection in prey and more vulnerability of infected prey to predation. The combined harvesting of both species along with disease related death of prey has also been taken into account. It has been observed that the parameter concerned with disease related death affects the endemic state. Threshold numbers along with stability are also discussed. The contributions of Hethcote et. al.7 and Trivedi et. al.12 follows as corollary.

KEYWORDS: Prey-Predator model, Epidemiological model, Stability

B. CHALUVARAJU
Department of Mathematics, Bangalore University, Jnanabharathi Campus Bangalore – 560 056 (India)
M. KUMARA
Department of Mathematics, Bangalore University, Jnanabharathi Campus Bangalore – 560 056 (India)

ABSTRACT:

The packing chromatic number χ$_{p}$(G) of a graph G = (V,E) is the smallest integer k such that the vertex set V(G) can be partitioned into disjoint classes V1 ,V2 ,…,V, where vertices in Vhave pairwise distance greater than i. In this paper, we compute the packing chromatic number of circulant graphs with different jump sizes.$_{}$

KEYWORDS: Coloring, ; Packing chromatic number, Circulant graph, AMS Subject Classification: 05C15, 05E30

The packing chromatic number χ(G) of a graph G = (V,E) is the smallest integer k such that the vertex set V(G) can be partitioned into disjoint classes V1 ,V2 ,…,Vk ,...

V.R. KULLI
Department of Mathematics Gulbarga University, Gulbarga 585106 (India)
B. CHALUVARAJU
Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore-560 056 (India)
T.V. ASHA
Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore-560 056 (India)

ABSTRACT:

Chemical graph theory is a branch of graph theory whose focus of interest is to finding topological indices of chemical graphs which correlate well with chemical properties of the chemical molecules. In this paper, we compute the Nirmala index, first and second inverse Nirmala indices for some chemical networks like silicate networks, chain silicate networks, hexagonal networks, oxide networks and honeycomb networks along with their comparative analysis.

KEYWORDS: Nirmala index, first and second inverse Nirmala indices,, chemical networks., Mathematics Subject Classification: 05C09, 05C92, 92E10.

SUBHASH KUMAR SHARMA
Department of Electronics, M.G.P.G. College, Gorakhpur (India)
SHRI PRAKASH DUBEY
Department of Physics , M.G.P.G. College, Gorakhpur (India)
ANIL KUMAR MISHRA
Department of Physics , M.G.P.G. College, Gorakhpur (India)

ABSTRACT:

This paper deals with development of an n-bit binary to decimal conversion, decimal to n bit binary conversion and decimal to IEEE-754 conversion for floating point arithmetic logic unit (FPALU) using VHDL. Normally most of the industries now a days are using either 4-bit conversion of ALU or 8-bit conversions of ALU, so we have generalized this, thus we need not to worry about the bit size of conversion of ALU. It has solved all the problems of 4-bit, 8-bit, 16-bit conversions of ALU’s and so on. Hence, we have utilized VHSIC Hardware Description Language and Xilinx in accomplishing this task of development of conversions processes of ALU

KEYWORDS: Binary, Decimal conversion, Floating point representation, Simulations and Device Utilization

SUSHIL KUMAR
Department of Mathematics & Astronomy, University of Lucknow- Lucknow,U. P. (India)

ABSTRACT:

Production inventory models have an important role in production planning and scheduling. In any economic production quantity (EPQ) model, the production rate is dependent on demand. In this paper we have established a production inventory model for perishable items with partial backlogging and time dependent exponential demand rate. Allowing shortage, it is partially backlogged. The unsatisfied demand is backlogged and it is considered a function of waiting time. The aim of our study is to optimizing the total profit during a given cycle. A numerical example is given in showing the applicability of the developed model.

KEYWORDS: Inventory, , Backlogging and Time Dependent Exponential Demand Rate, Perishability, Subject Classification- MSC 2010 (90B05)

BANASHREE BORA
Assistant Professor, Department of Mathematics, Kakojan College, Jorhat, Assam (ICHANDRA CHUTIA
Associate Professor, Department of Mathematics, Jorhat Institute of Science and Technology (India)
PRANAB JYOTI BARMAN
Assistant Professor, Department of Civil Engineering, Jorhat Institute of Science and Technology (India)

ABSTRACT:

In the present day scenario, in developing countries, solid waste management is declared as a dangerous issue. Population explosion, high standard of living, urbanization, lack of knowledge about management of waste etc. are the main cause of waste generation. An educational institution can play an important role in terms of waste management. It is observed that environmental studies is being introduced in all programs as a subject from lower primary up to higher level with the objectives to make concern everyone about their nature from childhood but it could not fulfill the objectives in deed. In this paper we propose a mathematical model using linear programming to manage the solid waste of an educational institution with minimum cost within the limited facilities there in.

KEYWORDS: Linear programming, Solid waste, ,Sensitivity analysis, AMS CLASSIFICATION: 90C05, 90C31.

V. VIJAYAKUMAR
B-111, Saivihar, Sector-15, CBD-Belapur, NaviMumbai-400614 (India)

ABSTRACT:

The measured thermal radiation from a material surface will, in general, have a wave length ($\lambda$) dependent scale-factor to the Planck profile (PT) from the contributions of the emissivity (Є$\lambda$) of the surface, the response function (A$\lambda$) of the measurement setup, and the emission via non-Plank processes. For obtaining the absolute temperature from such a profile, a procedure that take care of these dependencies and which relay on a temperature grid searchis proposed. In the procedure, the deviation between the Plank profiles at various temperatures and the measured spectrum that is made equal to it at a selected wavelength, by scaling, is used. The response function (A$\lambda$) is eliminated at the measurement stage and the polynomial dependence of the remnant scale factor mostly dominated by Є$\lambda$) i s extracted from the measured spectrum by identifying its optimal $\lambda$ dependence. It is shown that when such a computation is carried out over a temperature grid, the absolute temperature can be identified from the minimum of the above deviation. Here, search for T and Є$\lambda$) d elinked, unlike in the leastsquare approaches that are normally employed. Code that implements the procedure is tested with simulated Planck profile to which different viable values of Є$\lambda$) a nd noise is incorporated. It shown that if the $\lambda$ dependence of scale-factor is not too high, the absolute temperature can be recovered. A large $\lambda$ dependent scale-factor and the consequent possible error in the temperature obtained can also be identified.

KEYWORDS: Planck profile, Absolute Temperature scale, Temperature measurement

K. SREERAM REDDY
Department of Mathematics, Osmania University, Hyderabad, Telangana-500007-India
Ch. MAHESH
Department of Mathematics, Osmania University, Hyderabad,Telangana-500007-India

ABSTRACT:

Mathematical model has been developed to protect fluid and solid particle homogeneous mixture velocity concentration and temperature for a heated horizontal flat plate. Conversation equation based on Eulerian scale are approximated for small relaxation times through stream function and similarity transformations. Parametric database generated through computer program for arbitrary constants on comparison with clear fluid reveals the particle concentration has pronounced effect on velocity and temperature profiles.

KEYWORDS: Fluid Mechanics, Boundary layer equations, ordinary differential equation, AMS Subject Classification: 35Q35 37N10, 76A04, 78M15

V. R. KULLI
Department of Mathematics, Gulbarga University, Gulbarga – 585 106 (India)
B. CHALUVARAJU
Department of Mathematics, Bangalore University, Jnanabharathi Campus Bangalore -560 056 (India)
M. KUMARA
Department of Mathematics, Bangalore University, Jnanabharathi Campus Bangalore -560 056 (India)

ABSTRACT:

The disjoint total restrained domination number of a graph G is the minimum cardinality of the union of two disjoint total restrained dominating sets in G. We also consider an invariant the minimum cardinality of the disjoint union of a restrained dominating set and a total restrained dominating set. In this paper, we initiate a study of these parameters and establish some results on these new parameters.

KEYWORDS: Inverse domination set, restrained dominating set, total restrained dominating set

SANJIT KU. MOHANTY
Head of Department of Mathematics B.S. Degree College, Nuahat, Jajpur-754296,Odisha (India)
RAJANI BALLAV DASH
Visiting Faculty, Department of Mathematics, Ravenshaw University, Cuttack, Odisha (India)

ABSTRACT:

A mixed quadrature rule of precision nine for approximate evaluation of real definite integrals has been constructed by blending Clenshaw-Curtis five point rule modified by Richardson Extrapolation and GaussLegendre four point rule. An error analysis for this mixed rule is provided. The efficiency of this rule is highlighted through numerical evaluation of some definite integrals at the end.

KEYWORDS: Clenshaw-Curtis quadrature rule, Gauss-Legendre 4-point rule, Richardson Extrapolation, Subject classification: 65D32