# Journal of Mathematics Research

Online ISSN: 1916-9809
Publications
Article
In this paper we present two efficient approximations for the complex error function $w \left({z} \right)$ with small imaginary argument $\operatorname{Im}{\left[{z} \right]} < < 1$ over the range $0 \le \operatorname{Re}{\left[{z} \right]} \le 15$ that is commonly considered difficult for highly accurate and rapid computation. These approximations are expressed in terms of the Dawson's integral $F\left(x \right)$ of real argument $x$ that enables their efficient implementation in a rapid algorithm. The error analysis we performed using the random input numbers $x$ and $y$ reveals that in the real and imaginary parts the average accuracy of the first approximation exceeds ${10^{- 9}}$ and ${10^{- 14}}$, while the average accuracy of the second approximation exceeds ${10^{- 13}}$ and ${10^{- 14}}$, respectively. The first approximation is slightly faster in computation. However, the second approximation provides excellent high-accuracy coverage over the required domain.

Article
Physical meaning and a duality of concepts of wave function, action functional, entropy, the Pointing vector, the Einstein tensor and so on can be disclosed by investigating the state of material systems such as thermodynamic and gas dynamic systems, systems of charged particles, cosmologic systems and others. These concepts play a same role in mathematical physics. They are quantities that specify a state of material systems and also characteristics of physical fields. The duality of these concepts reveals in the fact that they can at once be both functionals and state functions or potentials. As functionals they are defined on nonintegrable manifold (for example, on tangent one), and as a state function they are defined on integrable manifold (for example, on cotangent one). The transition from functionals to state functions dicribes the mechanism of physical structure origination. The properties of these concepts can be studied by the example of entropy and action. The role of these concepts in mathematical physics and field theory will be demonstrated. Such results have been obtained by using skew-symmetric forms. In addition to exterior forms, the skew-symmetric forms, which are obtained from differential equations and, in distinction to exterior forms, are evolutionary ones and are defined on nonintegrable manifolds, were used. Comment: 17 pages

Article
Landau-Kolmogorov inequalities have been extensively studied on both continuous and discrete domains for an entire century. However, the research is limited to the study of functions and sequences on $\Bbb R$ and $\Bbb Z$, with no equivalent inequalities in higher-dimensional spaces. The aim of this paper is to obtain a new class of discrete Landau-Kolmogorov type inequalities of arbitrary dimension: $$\|\varphi\|_{\ell^\infty(\Bbb Z^d)} \leq \mu_{p,d}\|\nabla_D\varphi\|^{p/2^d}_{\ell^2(\Bbb Z^d)}\, \|\varphi\|^{1-p/2^d}_{\ell^2(\Bbb Z^d)}, %$$ where the constant $\mu_{p,d}$ is explicitly specified. In fact, this also generalises the discrete Agmon inequality to higher dimension, which in the corresponding continuous case is not possible.

Article
We introduce some analytic relations on the set of partial differential equations of two variables. It relies on a new comparison method to give rough asymptotic estimates for solutions which obey different partial differential equations. It uses a kind of scale transform called tropical geometry which connects automata with real rational dynamics. Two different solutions can be considered when their defining equations are transformed to the same automata at infinity. We have a systematic way to construct related pairs of different partial differential equations, and also construct some unrelated pairs concretely. These verify that the new relations are non trivial. We also make numerical calculations and compare the results for both related and unrelated pairs of PDEs.

Article
We present a rational approximation for rapid and accurate computation of the Voigt function, obtained by residue calculus. The computational test reveals that with only $16$ summation terms this approximation provides average accuracy ${10^{- 14}}$ over a wide domain of practical interest $0 < x < 40,000$ and ${10^{- 4}} < y < {10^2}$ for applications using the HITRAN molecular spectroscopic database. The proposed rational approximation takes less than half the computation time of that required by Weideman's rational approximation. Algorithmic stability is achieved due to absence of the poles at $y \geqslant 0$ and $- \infty < x < \infty$.

Article
In this paper we revisit the mild-solution approach to second-order semi-linear PDEs of Hamilton-Jacobi type in infinite-dimensional spaces. We show that a well-known result on existence of mild solutions in Hilbert spaces can be easily extended to non-autonomous Hamilton-Jacobi equations in Banach spaces. The main tool is the regularizing property of Ornstein-Uhlenbeck transition evolution operators for stochastic Cauchy problems in Banach spaces with time-dependent coefficients

Article
Let $D$ be a bounded domain in a complex Banach space. According to the Earle-Hamilton fixed point theorem, if a holomorphic mapping $F : D \mapsto D$ maps $D$ strictly into itself, then it has a unique fixed point and its iterates converge to this fixed point locally uniformly. Now let $\mathcal{B}$ be the open unit ball in a complex Hilbert space and let $F : \mathcal{B} \mapsto \mathcal{B}$ be holomorphic. We show that a similar conclusion holds even if the image $F(\mathcal{B})$ is not strictly inside $\mathcal{B}$, but is contained in a horosphere internally tangent to the boundary of $\mathcal{B}$. This geometric condition is equivalent to the fact that $F$ is asymptotically strongly nonexpansive with respect to the hyperbolic metric in $\mathcal{B}$.

Article
The main drawback of the Frenet frame is that it is undefined at those points where the curvature is zero. Further- more, in the case of planar curves, the Frenet frame does not agree with the standard framing of curves in the plane. The main drawback of the Bishop frame is that the principle normal vector N is not in it. Our new frame, which we call the Beta frame, combines, on a large set of curves, the best aspects of the Bishop frames and the Frenet frames. It yields a globally defined normal, a globally defined signed curvature, and a globally defined torsion. For planar curves it agrees with the standard framing of curves in the plane.

Article
We present a new family of embedded doubly periodic minimal surfaces, of which the symmetry group does not coincide with any other example known before.

Article
In order to approximate the integral $I(f)=\int_a^b f(x) dx$, where $f$ is a sufficiently smooth function, models for quadrature rules are developed using a given {\it panel} of $n (n\geq 2)$ equally spaced points. These models arise from the undetermined coefficients method, using a Newton's basis for polynomials. Although part of the final product is algebraically equivalent to the well known closed Newton-Cotes rules, the algorithms obtained are not the classical ones. In the basic model the most simple quadrature rule $Q_n$ is adopted (the so-called left rectangle rule) and a correction $\tilde E_n$ is constructed, so that the final rule $S_n=Q_n+\tilde E_n$ is interpolatory. The correction $\tilde E_n$, depending on the divided differences of the data, might be considered a {\em realistic correction} for $Q_n$, in the sense that $\tilde E_n$ should be close to the magnitude of the true error of $Q_n$, having also the correct sign. The analysis of the theoretical error of the rule $S_n$ as well as some classical properties for divided differences suggest the inclusion of one or two new points in the given panel. When $n$ is even it is included one point and two points otherwise. In both cases this approach enables the computation of a {\em realistic error} $\bar E_{S_n}$ for the {\it extended or corrected} rule $S_n$. The respective output $(Q_n,\tilde E_n, S_n, \bar E_{S_n})$ contains reliable information on the quality of the approximations $Q_n$ and $S_n$, provided certain conditions involving ratios for the derivatives of the function $f$ are fulfilled. These simple rules are easily converted into {\it composite} ones. Numerical examples are presented showing that these quadrature rules are useful as a computational alternative to the classical Newton-Cotes formulas.

Article
Let $\rho = \sigma + i \tau$ be a nontrivial zero of the Riemann zeta-function. In this note, we first present a certain condition on the zero-free region of the Riemann zeta-function such that if it were shown to be satisfied, then it would follow that $\sigma \to 1/2$ as $\tau \to \infty$. Furthermore, we discuss an argument of computational nature regarding the Riemann hypothesis.

Article
By only using spectral theory of the Laplace operator on spheres, we prove that the unit 3-dimensional sphere of a 2-dimensional complex subspace of $\mathbb{C}^3$ is a $\Omega$-stable submanifold with parallel mean curvature, when $\Omega$ is the K\"ahler calibration of rank 4 of $\mathbb{C}^3$.

Article
In this paper, we shall give a set R* and indicate its properties, and thus, some abnormal results, such as thelimit number may be successor, the natural number may be transfinite, the infinite set can not be equipotent toits proper subset etc., will be obtained.

Article
Understanding the formation and evolution of alimentary consumption patterns requires a broad and multidimensionalapproach. Foods originate either from plants and animals, representing the living processes, or agriculture and industry,representing the non-living processes, and in these forms they play their biological role. Additionally, the consumptionof foods has multiple consequences (social, economic, health, etc.) on an individual level as well as on a wider collectivelevel. In this essay we attempt to describe alimentary consumption patterns in Greece (1957-2005) from three differentdimensions: a natural dimension (animal or plant origin), a technical one (agricultural or industrial origin) and finally, abiological one (nutritional properties). The description, which we will use as the foundation to create an interpretativetheory, is done through charts and tables, based on numerical indicators that are deduced from simple illustrative functions.Tables used in the present paper are either simple or double-entry and we present spreading diagrams as well.

Article
Let G = (V; E) be a connected graph. For integers j ? k, L( j; k)-labeling of a graph G is an integer labeling of the vertices in V such that adjacent vertices receive integers which differ by at least j and vertices which are at distance two apart receive labels which differ by at least k. In this paper we discuss L(2; 1) labeling (or distance two labeling) in the context of some graph operations.

Article
Journal of Mathematics Research, Vol. 1, No. 1, March 2009

Article
Journal of Mathematics Research, Vol. 2, No. 1, March 2010, all in one file.

Article
Focusing on several crisis-hit East-Asian countries, this paper seeks to uncover the main source of shocks and its link tothe performance of policy regime in these countries between the two sub-periods of pre- and post-crisis. A comparativestructural VAR analysis is conducted to study the dynamic of shocks. The results show that the economies of East-Asiancountries are mainly driven by domestic shocks and shocks are asymmetric. External shocks have low effects on domesticvariables but they are increasing over time. Given that real exchange rate reacts stronger to real economy but lower to itsown shock, and that the economies tend to experience real depreciation and lower volatility in inflation in the post-crisisperiod, the results imply more effective policy and greater role of exchange rate to act as a shock absorber under floatingexchange rate regimes aftermath the crisis.

Article
All-optical shared fiber-delay-line (FDL) packet switches have been studied intensively in the literature and with theliterature, many scheduling genetic algorithms have been proposed. However, these genetic algorithms suffer from notbeing able to provide a delay bound, or require complex timing methods to compute scheduling assignments. In thispaper, we propose two fast scheduling algorithms for all-optical shared-FDL packet switches. In the first algorithm,packet scheduling is formulated as a tree-searching problem. This is accomplished by breaking down the search tree intomultiple smaller subsets and assigning each subset to a parallel processor. By using this method, scheduling solutions canbe obtained in a shorter time. Although this approach is superior to other algorithms, its overall complexity and processingoverheads are still too high to warrant its day to day use. In the second algorithm, the search tree is carefully trimmeddown in order to reduce complexity and overheads. The conclusion will consider a 32 × 32 switch with 32 FDLs, andassume a processor clock rate of 200MHz for schedulers. With this new and second algorithm, a scheduling assignmentcan be calculated for a given packet in 30ns if 8 parallel processors are employed and we show by simulation that bothalgorithms can achieve a loss rate of ? 10?7 even at load 0.9, where the average delay is 11.5 timeslots.

Article
This paper presents a new approach to Automatic Differentiation (AD) for a scalar valued and twice continuouslydifferentiable function f : R^n - R. A new arithmetic is obtained based on the chain rule and usingaugmented algebra of real numbers. The chain rule based differentiation arithmetic is used to find the Gradientand Hessian. Jacobian is evaluated using Gradient arithmetic by computing Gradient for components and is arrangedin matrix form to give Jacobian value. The resulting derivative evaluation uses the operator overloadingconcept which uses computer programs written in C++.

Article
The adjoint matrix is an important concept of matrix theory, it can deduce the formula for calculating the inverse matrix of a square matrix, thus solving the problem of inverse square. At the same time, the properties of the matrix are very important. As a partition of a matrix into rectangular smaller matrices, the operation of a matrix can be transferred to the block matrix, making the operation more convenient. We obtain some operation properties of adjoint matrices of a kind of block matrices by means of basic properties of adjoint matrices.

Article
It is well-known that futures transaction of negotiable securities and stocking are highly risky. How to prevent the risk isvery important for the investor. During the actual investment, the capability of controlling risk is often showed throughthe capability of risk assessment. Up-to-date, many researchers are only limited to study one variable about it. In thispaper, based on the actual transaction, discussing many uncertain factors and probability characters, applying extremumtheory and considering fully the uncertainty from the price volatilities of futures, the new model of risk alarming is given.

Article
The construction of the integers introduced by Dedekind is an algebraic one. Subtraction can not be done without restrictionin natural numbers N. If we consider the definition of multiplication of integral domain Z, N with respect tosubtraction is needed. It is necessary to give the definition of subtraction in N. Instead of starting from natural numbers,one could begin with any commutative semi-group and construct from it as the construction of the integers to obtain acommutative group. If the cancellation law does not hold in the commutative semi-group, some modifications are required.The mapping from the commutative semi-group to the commutative group is not injective and compatible withaddition. In the relation between real numbers and decimals, N also plays an important role.

Article
In this paper we have introduce fuzzy quasi-ideal and fuzzy left(right, two-sided) ideals in LA-semigroup. We have proved some results related to fuzzy quasi-ideals and fuzzy left(right, two-sided) ideals of an LA-semigroup. Further we characterize an intra-regular LA-semigroup by the properties of their fuzzy ideals.

Article
We introduce anti fuzzy quasi-ideals, anti fuzzy bi-(generalized bi-)ideals and anti fuzzy left (right, two-sided) ideals in LA-semigroup. Further we characterize intra-regular LA-semigroups by the properties of their anti fuzzy left (right, two-sided) ideals, anti fuzzy bi-(generalized bi-)ideals, anti fuzzy interior ideals and anti fuzzy quasi-ideals. Further we show that anti fuzzy two-sided ideals, anti fuzzy bi-ideals, anti fuzzy generalized bi-ideals, anti fuzzy interior ideals and anti fuzzy quasi-ideals coincide in an intra-regular LA-semigroup with left identity. Also we prove that the set of anti fuzzy two-sided ideals of an intra-regular LA-semigroup S with left identity forms a semilattice structure.

Article
In this paper we have studied the concept of Anti fuzzy ideals in Left Almost Semigroups (LA-semigroup in short). The equivalent statement for an LA-semigroup to be a commutative semigroup is proved. The set of all anti fuzzy left ideals, which are idempotents, forms a commutative monoid. Moreover it has been shown that the union of any family of Anti fuzzy left ideals of an LA-semigroup is an anti fuzzy left ideal of F(S). The relation of anti fuzzy left(right) ideals, anti fuzzy interior ideals and anti fuzzy bi-ideals in LA-semigroups has been studied. Anti fuzzy points have been defined in an LA-semigroup and has been shown the representation of largest fuzzy left ideal generated by a fuzzy point.

Article
The present paper represents an analytical solution of fingering phonomenon arising in double phase flow through homogeneousmedia under certain initial & boundary condition using techniques of calculus of variation and similarity theory.The numerical and graphical representation of solution has been given the graph of saturatin F(?) of injected liquid, isincreasing after ? = 0.5 for t > 0, which indicates that when injected liquid entries into native liquid at common-interface,then suddenly the native liquid enters into injected liquid due to difference in wettability. Hence initial saturation willdecrease and then after ? > 0.5 the saturation uniformly increases parabolically which is physically consistent with theavailable theory.

Article
The Making the experiment on electromagnetic launcher, the rail supported by the containment and the insulator is modeledas a cantilever beam of finite length sitting on the elastic foundation. The mathematical model and the dynamicequation of the rail is given in the loading condition, as well as the analytical solution of the equation. The study willpaves the way for mathematic model building and solution of rail gun with uneven pressure.

Article
The moving least-square technique is used to construct shape function in the Element Free Galerkin Methodat present, but sometimes the algebra equations system obtained from the moving least-square approximationis ill-conditioned and the shape function needs large quantity of inverse operation. In this paper, the weightedorthogonal functions are used as basis ones, the application in the calculation of plate bending shows that theimproved moving least-square approximation is effective and efficient.

Article
There is a need to fully appreciate the legacy of Malaysia urbanization on aordable housing since the proportions ofurban population to total population in Malaysia are expected to increase up to 70% in year 2020. This study focusedin Johor Bahru, Malaysia one of the highest urbanized state in the country. Monthly time-series data have been usedto forecast the demand on low-cost housing using Artificial Neural Networks approach. The dependent indicator is thelow-cost housing demand and nine independents indicators including; population growth; birth rate; mortality baby rate;inflation rate; income rate; housing stock; GDP rate; unemployment rate and poverty rate. Principal Component Analysishas been adopted to analyze the data using SPSS package. The results show that the best Neural Network is 2-22-1 with0.5 learning rate and momentum rate respectively. Validation between actual and forecasted data show only 16.44% ofMAPE value. Therefore Neural Network is capable to forecast low-cost housing demand in Johor Bahru, Malaysia.

Article
In this paper we have defined anti fuzzy interior ideal in semigroups. We characterize regular, intra-regular and left (right)quasi-regular semigroups by the properties of their anti fuzzy ideals, anti fuzzy bi-ideals, anti fuzzy generalized bi-ideals,anti fuzzy interior ideals and anti fuzzy quasi-ideals.

Article
The nonlinear K(n, 1) equation with weak damping is investigated via the approximate symmetry perturbation method andapproximate direct method. The approximate symmetry and similarity reduction equations of different orders are derivedand the corresponding series reduction solutions are obtained. As a result, the formal coincidence for both methods isdisplayed.

Article
We propose approximations to the normal distribution function and to its inverse function using single polynomials ineach case. The absolute error of these approximations is significantly less than those of other approximations availablein the literature. We compare all the polynomial approximations empirically by calculating their respective percentageabsolute relative errors.

Article
Research into Wavelet Neural Networks was conducted on numerous occasions in the past. Based on previous research,it was noted that the Wavelet Neural Network could reliably be used for function approximation. The research conductedincluded comparisons between the mother functions of the Wavelet Neural Network namely the Mexican Hat, GaussianWavelet and Morlet Functions. The performances of these functions were estimated using the Normalised Square RootMean Squared Error (NSRMSE) performance index. However, in this paper, the Root Mean Squared Error (RMSE)was used as the performance index. In previous research, two of the best mother wavelets for function approximationswere determined to be the Gaussian Wavelet and Morlet functions. An in-depth investigation into the two functions wasconducted in order to determine which of these two functions performed better under certain conditions. Simulationsinvolving one-dimension and two-dimension were done using both functions. In this paper, we can make a specificallyinterpretation that Gaussian Wavelet can be used for approximating function for the function domain [?1, 1]. WhileMorlet function can be used for big domain. All simulations were done using Matlab V6.5.

Article
This paper aims at constructing a two-phase iterative numerical algorithm for the improved approximation of a continuousfunction by the ‘Modified Szasz’ operator. The algorithm uses a ‘statistical perspective’ to more fully expoit the informationabout the unknown function f . The improvement occurs iteratively. A typical iteration uses the twin statisticalconcepts of ‘Mean Square Error’ (MSE) and ‘Bias’; the application of the latter concept being preceded by that of theformer in the algorithm. At any iteration, the statistical concept of ‘MSE’ is used in “Phase II”, after that of the ‘Bias’ in“Phase I”. The procedure is like a sandwich. The top and bottom slices are the operations of ‘Bias-Reduction’ in “PhaseI” of the algorithm, and the operation of ‘MSE-Reduction’ in “Phase II” is the stuffing in the sandwich. The improvementacheived by this algorithm is evaluated by means of a simulation study using known functions. The simulation has beenconfined to three iterations only, for the sake of simplicity.

Article
Latin hypercube sampling(LHS)(McKay, M.D., 1979) is a method of sampling that can be used to estimate the value ofmultidimensional integration. Loh(Loh, W.L., 1996b) and Neammanee and Rattanawong(Neammanee, K., 2009) gave auniform bound in normal approximation for LHS. In this paper, we give a non-uniform bound of this approximation byusing Stein’s method.

Article
The Extended Euclidean algorithm for matrix Pade approximants is applied to compute matrix Pade approximants in rectangularfull packed format (RFP) if the coefficient matrices of the input matrix polynomial are triangular. The proceduregiven by Gustavson et al for packing a triangular matrix in rectangular full packed format is applied to pack sequenceof lower triangular matrices of a matrix polynomial in Rectangular Full Packed format. This RFP format of a matrixpolynomial is applied to compute matrix Pade approximants of the matrix polynomial using Matrix Pade Extended EuclideanAlgorithm. Algorithms for the multiplication of two triangular matrices and inverse of a triangular matrix in RFPformat are also presented. The CPU time and memory comparison in computing the matrix Pade approximants of a matrixpolynomial between RFP format case and non packed case are elucidated in detail.

Article
We prove common fixed point theorems for weakly compatible mappings satisfying a generalized contraction principle byusing a control function. As an application, we have established invariant approximation result. Our theorems generalizerecent results existing in the literature.

Article
Based on the Newton-Cotes and Gaussian quadrature rules, we develop several new closed form approximations to the mathematical constant e. For validating effectiveness of our approximations, a comparison of our results to the existing approximations is also presented. Because of the level of mathematics, the presented work is easily embraceable in an undergraduate class. Another aim of this work is to encourage students for formulating other better approximations by using the suggested strategy.

Article
We investigate some new results for strongly multiplicative labeling of graph. We prove that the graph obtained by arbitrary supersubdivision of tree $T$, grid graph $P_{n}imes P_{m}$, complete bipartite graph $K_{m,n}$, $C_{n}odot P_{m}$ and one-point union of $m$ cycle of length $n$ are strongly multiplicative.

Article
In the condition that the real valued function f : S ? R is a arc connected function in arc connected set S ? Rn, thispaper give the definition of generalized arc connected function. The class function is the promotion of convex functionwhich satisfies identified local-global extremum property. Conversely, under certain conditions. the function meetinglocal-global extremum property must be one of those generalized functions. Also, the optimality sufficient condition ofminx?S f (x), s.t.g(x) ? 0 is obtained under generalized connected assumption.

Article
The oscillation of second order neutralequations with distributed deviating arguments is studied. By usinga class of parameter functions $Phi(t,s,l)$ and the generalizedRiccati technique, some new oscillation criteria for the equationsare obtained. The obtained results are different from most knownones and can be applied to many cases which are not covered byexisting results. Two examples are also included to show thesignificance of our results.

Article
The application of multivariate time series is so large,it can be used in many systems, like ecnomic systems,biologicalsystems, and so on.This paper introduced the method’s building and the structure of ARIMAX model (auto-regressiveintegrated moving average model with explanatory variables) and its SAS realizing. The paper analysed the tertiaryindustryin China with the realty business to be input variable and proved that there had been co-integration relationshipbetween the two time serieses. Then, the paper modeled an appropriate ARIMAX model to tertiary-industry and fitthis model with the real statistics(the tertiary-industry’s production values in China from 1978 to 2007). And the resultshowed that ARIMAX, applied ARIMAX model to analyzing and forecasting of tertiary-industry, it is a model with highprediction precision.

Article
Let f be an integrable function from R3 to R and μ = )[0,1]3 f (x)dx. A simple estimator of μ is ˆμ =1nn *i=1f ? Xi whereX1, X2, ...Xn are independent random vectors and uniformly distributed on [0, 1]3. In 2006, Neammanee and Laipapornused the orthogonal array to choose the points Xi’s and established a non-uniform concentration inequality. In this article,we improve their result.

Article
In this paper the mathematical model has been developed to evaluate wall shear stress in the stenosis of artery. The arteryis modeled as symmetric stenosis vessel; also the flow of blood is modeled as an incompressible Newtonian fluid. Theresults show that shear stress have direct proportional relation with both length and height of stenosis. This mathematicalmodel is a useful and a simple toll to evaluate wall shear stress of patients with stenosis artery disease.

Article
The paper employs Artificial Neural Network (ANN) to forecast foreign exchange rate in India during 1992-2009. We used two types of data set (daily and monthly) for US dollar, British pound, euro and Japanese yen. The performance of forecasting is quantified by using various loss functions namely root mean square error (RMSE), mean absolute error (MAE), mean absolute deviation (MAD) and mean absolute percentage error (MAPE). Empirical results confirm that ANN is an effective tool to forecast the exchange rate. The technique gives the evidence that there is possibility of extracting information hidden in the foreign exchange rate and predicting it into the future. The evaluation of the proposed model is based on the estimation of the average behaviour of the above loss functions.Keywords- Exchange Rate; Neural Network

Article
Using Markov chain model and by the changes of state transition about system, this paper describes the dynamic characteristicsof teaching method of the basis course in the engineering institutions, which reflects the management of institutionsand eect of teaching and learning.

Article
This paper presents some modifications of Ford-Fulkerson’s labeling method for solving the maximal network flow problemwith application in solving the transportation and assignment problems. The modifications involve the tree representationof the nodes labeled and the edges used them. It is shown that after each flow adjustment some of the labels canbe retained for the next labeling process. Through certain computational aspects it has been suggested that to indicatethat with theses the primal-dual approach for solving the transportation and assignment problems is improved to certainextent.

Article
The purpose of this article is to prove strong convergence theorems for mapping of asymptotically quasi-nonexpansivetypes in a Hilbert space according to hybrid methods. The results obtained in this paper extend and improve upon thoserecently announced by Qin, X., Su, Y. and Shang, M. (Qin, X. et al., 2008), and many others.

Article
This paper describes a single species model, which followed by two stages, a mature and an immature stage. Conditionsfor existence of equilibrium points and their stability are discussed. The model in this paper has been developed on theconcept of optimal management of resources based on the criterion of maximization of present values of net economicrevenues. Using the data from the North-East Atlantic cod fishery, the results of the optimal stock, harvest and effort levelare derived. Our simulation results show that optimal harvesting policy is much superior than the MSY policy and optimalpaths always take less time than the suboptimal path to reach the optimal steady state. Our analysis also shows that, if itis insisted that a closure is take place for one of the two sub-stocks,it will be optimal to reduce fishing on the immaturesub-stock rather than the mature sub-stock.

Top-cited authors
• Saurashtra University
• INTI International University
• Sri Paramakalyani College,Manonmaniam Sundaranar University
• Hemchandracharya North Gujarat University
• Universiti Brunei Darussalam