International Journal of Mathematics and Mathematical Sciences
[SJR: 0.346] [H-I: 27] [3 followers] Follow
Open Access journal
ISSN (Print) 0161-1712 - ISSN (Online) 1687-0425
Published by Hindawi [334 journals]
- A Note on the Performance of Biased Estimators with Autocorrelated Errors
Abstract: It is a well-established fact in regression analysis that multicollinearity and autocorrelated errors have adverse effects on the properties of the least squares estimator. Huang and Yang (2015) and Chandra and Tyagi (2016) studied the PCTP estimator and the class estimator, respectively, to deal with both problems simultaneously and compared their performances with the estimators obtained as their special cases. However, to the best of our knowledge, the performance of both estimators has not been compared so far. Hence, this paper is intended to compare the performance of these two estimators under mean squared error (MSE) matrix criterion. Further, a simulation study is conducted to evaluate superiority of the class estimator over the PCTP estimator by means of percentage relative efficiency. Furthermore, two numerical examples have been given to illustrate the performance of the estimators.
PubDate: Mon, 30 Jan 2017 06:34:57 +000
- On Killing Forms and Invariant Forms of Lie-Yamaguti Superalgebras
Abstract: The notions of the Killing form and invariant form in Lie algebras are extended to the ones in Lie-Yamaguti superalgebras and some of their properties are investigated. These notions are also -graded generalizations of the ones in Lie-Yamaguti algebras.
PubDate: Thu, 12 Jan 2017 09:34:48 +000
- Modal Logic Axioms Valid in Quotient Spaces of Finite CW-Complexes and
Other Families of Topological Spaces
Abstract: In this paper we consider the topological interpretations of , the classical logic extended by a “box” operator interpreted as interior. We present extensions of S4 that are sound over some families of topological spaces, including particular point topological spaces, excluded point topological spaces, and quotient spaces of finite CW-complexes.
PubDate: Mon, 26 Dec 2016 06:01:11 +000
- Vector Spaces of New Special Magic Squares: Reflective Magic Squares,
Corner Magic Squares, and Skew-Regular Magic Squares
Abstract: The definition of a regular magic square motivates us to introduce the new special magic squares, which are reflective magic squares, corner magic squares, and skew-regular magic squares. Combining the concepts of magic squares and linear algebra, we consider a magic square as a matrix and find the dimensions of the vector spaces of these magic squares under the standard addition and scalar multiplication of matrices by using the rank-nullity theorem.
PubDate: Wed, 30 Nov 2016 11:17:13 +000
- Some Remarks on Quasi-Generalized CR-Null Geometry in Indefinite Nearly
Abstract: Attention is drawn to some distributions on ascreen Quasi-Generalized Cauchy-Riemannian (QGCR) null submanifolds in an indefinite nearly cosymplectic manifold. We characterize totally umbilical and irrotational ascreen QGCR-null submanifolds. We finally discuss the geometric effects of geodesity conditions on such submanifolds.
PubDate: Mon, 14 Nov 2016 11:09:29 +000
- Symmetric Integer Matrices Having Integer Eigenvalues
Abstract: We provide characterization of symmetric integer matrices for rank at most 2 that have integer spectrum and give some constructions for such matrices of rank 3. We also make some connection between Hanlon’s conjecture and integer eigenvalue problem.
PubDate: Mon, 07 Nov 2016 09:33:15 +000
- Double Laplace Transform Method for Solving Space and Time Fractional
Abstract: Double Laplace transform method is applied to find exact solutions of linear/nonlinear space-time fractional telegraph equations in terms of Mittag-Leffler functions subject to initial and boundary conditions. Furthermore, we give illustrative examples to demonstrate the efficiency of the method.
PubDate: Wed, 26 Oct 2016 14:31:29 +000
- Quasi-Positive Delta Sequences and Their Applications in Wavelet
Abstract: A sufficient literature is available for the wavelet error of approximation of certain functions in the -norm. There is no work in context of multiresolution approximation of a function in the sense of sup-error. In this paper, for the first time, wavelet estimator for the approximation of a function belonging to class under supremum norm has been obtained. Working in this direction, four new theorems on the wavelet approximation of a function belonging to class using the projection of its wavelet expansions have been estimated. The calculated estimator is best possible in wavelet analysis.
PubDate: Tue, 25 Oct 2016 08:10:52 +000
- On Degrees of Modular Common Divisors and the Big Prime Algorithm
Abstract: We consider a few modifications of the Big prime modular algorithm for polynomials in . Our modifications are based on bounds of degrees of modular common divisors of polynomials, on estimates of the number of prime divisors of a resultant, and on finding preliminary bounds on degrees of common divisors using auxiliary primes. These modifications are used to suggest improved algorithms for calculation and for coprime polynomials detection. To illustrate the ideas we apply the constructed algorithms on certain polynomials, in particular on polynomials from Knuth’s example of intermediate expression swell.
PubDate: Wed, 05 Oct 2016 13:47:51 +000
- Modelling the Impact of Government Policies on Import on Domestic Price of
Indian Gold Using ARIMA Intervention Method
Abstract: The study attempts to determine the impact of government policies of import of gold in India on the domestic price of gold during 2013 using Autoregressive Integrated Moving Average (ARIMA) intervention model. 2013 was an amazing year for Indian gold market where the price had reached its zenith. In April 2013, to curb a record trade deficit, India imposed an import duty of 10 percent on gold and tied imports for domestic consumption to exports, creating scarce supply of the yellow metal and boosting premiums to curtail the Current Account Deficit (CAD). The objective of the paper is to model the impact of this intervention by the government on the domestic price of Indian gold. Suitable ARIMA model is fit on the preintervention period and thereafter the effects of the interventions are analysed. The results indicate that ARIMA is the most suitable model during preintervention period. Intervention analysis reveals that there is significant decrease in domestic price of gold by 56% from 2013. The model may be used by policymakers to analyse the future of gold before framing regulations and policies.
PubDate: Mon, 19 Sep 2016 09:29:59 +000
- Asymptotic Theory in Model Diagnostic for General Multivariate Spatial
Abstract: We establish an asymptotic approach for checking the appropriateness of an assumed multivariate spatial regression model by considering the set-indexed partial sums process of the least squares residuals of the vector of observations. In this work, we assume that the components of the observation, whose mean is generated by a certain basis, are correlated. By this reason we need more effort in deriving the results. To get the limit process we apply the multivariate analog of the well-known Prohorov’s theorem. To test the hypothesis we define tests which are given by Kolmogorov-Smirnov (KS) and Cramér-von Mises (CvM) functionals of the partial sums processes. The calibration of the probability distribution of the tests is conducted by proposing bootstrap resampling technique based on the residuals. We studied the finite sample size performance of the KS and CvM tests by simulation. The application of the proposed test procedure to real data is also discussed.
PubDate: Wed, 07 Sep 2016 16:41:19 +000
- Almost and Nearly Isosceles Pythagorean Triples
Abstract: This work is about extended pythagorean triples, called NPT, APT, and AI-PT. We generate infinitely many NPTs and APTs and then develop algorithms for infinitely many AI-PTs. Since AI-PT is of , we ask generally for PT satisfying for any . These triples are solutions of certain diophantine equations.
PubDate: Mon, 05 Sep 2016 14:12:51 +000
- Application of ADM Using Laplace Transform to Approximate Solutions of
Nonlinear Deformation for Cantilever Beam
Abstract: We investigate semianalytical solutions of Euler-Bernoulli beam equation by using Laplace transform and Adomian decomposition method (LADM). The deformation of a uniform flexible cantilever beam is formulated to initial value problems. We separate the problems into 2 cases: integer order for small deformation and fractional order for large deformation. The numerical results show the approximated solutions of deflection curve, moment diagram, and shear diagram of the presented method.
PubDate: Thu, 25 Aug 2016 16:58:19 +000
- Loan Transactions with Random Dates for the First and Last Periodic
Abstract: Usually, loan transactions contracted in practice are nonrandom; that is to say, all amounts received (principal) and paid (period instalments) by the borrower are previously agreed with the lender, as well as their respective dates. In this paper, two new alternative loan models are introduced, depending on whether the borrower survives or not to fulfil all repayment obligations. In this way, either the initial or the final date of repayments can be subject to this contingency. Additionally, the different parameters of such random transactions are determined, as well as several measures of profitability/cost for the lender/borrower, respectively. These transactions can be attractive for both the lender and the borrower, which therefore make them worthy of consideration and subsequent implementation for the benefit of both parties.
PubDate: Thu, 25 Aug 2016 16:02:32 +000
- Natural Partial Orders on Transformation Semigroups with Fixed Sets
Abstract: Let be a nonempty set. For a fixed subset of , let be the set of all self-maps on which fix all elements in . Then is a regular monoid under the composition of maps. In this paper, we characterize the natural partial order on and this result extends the result due to Kowol and Mitsch. Further, we find elements which are compatible and describe minimal and maximal elements.
PubDate: Sun, 21 Aug 2016 07:51:00 +000
- The Exponentiated Gumbel Type-2 Distribution: Properties and Application
Abstract: We introduce a generalized version of the standard Gumble type-2 distribution. The new lifetime distribution is called the Exponentiated Gumbel (EG) type-2 distribution. The EG type-2 distribution has three nested submodels, namely, the Gumbel type-2 distribution, the Exponentiated Fréchet (EF) distribution, and the Fréchet distribution. Some statistical and reliability properties of the new distribution were given and the method of maximum likelihood estimates was proposed for estimating the model parameters. The usefulness and flexibility of the Exponentiated Gumbel (EG) type-2 distribution were illustrated with a real lifetime data set. Results based on the log-likelihood and information statistics values showed that the EG type-2 distribution provides a better fit to the data than the other competing distributions. Also, the consistency of the parameters of the new distribution was demonstrated through a simulation study. The EG type-2 distribution is therefore recommended for effective modelling of lifetime data.
PubDate: Thu, 04 Aug 2016 12:20:17 +000
- Bessel Equation in the Semiunbounded Interval : Solving in the
Neighbourhood of an Irregular Singular Point
Abstract: This study expresses the solution of the Bessel equation in the neighbourhood of as the product of a known-form singular divisor and a specific nonsingular function, which satisfies the corresponding derived equation. Considering the failure of the traditional irregular solution constructed with the power series, we adopt the corrected Fourier series with only limited smooth degree to approximate the nonsingular function in the interval . In order to guarantee the series’ uniform convergence and uniform approximation to the derived equation, we introduce constraint and compatibility conditions and hence completely determine all undetermined coefficients of the corrected Fourier series. Thus, what we found is not an asymptotic solution at (not to mention a so-called formal solution), but a solution in the interval with certain regularities of distribution. During the solution procedure, there is no limitation on the coefficient property of the equation; that is, the coefficients of the equation can be any complex constant, so that the solution method presented here is universal.
PubDate: Sun, 31 Jul 2016 13:00:34 +000
- A 4-Point Block Method for Solving Higher Order Ordinary Differential
Abstract: An alternative block method for solving fifth-order initial value problems (IVPs) is proposed with an adaptive strategy of implementing variable step size. The derived method is designed to compute four solutions simultaneously without reducing the problem to a system of first-order IVPs. To validate the proposed method, the consistency and zero stability are also discussed. The improved performance of the developed method is demonstrated by comparing it with the existing methods and the results showed that the 4-point block method is suitable for solving fifth-order IVPs.
PubDate: Thu, 28 Jul 2016 14:57:28 +000
- Real Hypersurfaces of Nonflat Complex Projective Planes Whose Jacobi
Structure Operator Satisfies a Generalized Commutative Condition
Abstract: Real hypersurfaces satisfying the condition have been studied by many authors under at least one more condition, since the class of these hypersurfaces is quite tough to be classified. The aim of the present paper is the classification of real hypersurfaces in complex projective plane satisfying a generalization of under an additional restriction on a specific function.
PubDate: Wed, 27 Jul 2016 08:43:15 +000
- Univalent and Starlike Properties for Generalized Struve Function
Abstract: We derive conditions on the parameters , , and so that the function where is the normalized form of generalized Struve function, belongs to the class Also, some sufficient conditions for the function to be in the class are obtained.
PubDate: Thu, 14 Jul 2016 12:15:11 +000
- On the Commutative Rings with At Most Two Proper Subrings
Abstract: The commutative rings with exactly two proper (unital) subrings are characterized. An initial step involves the description of the commutative rings having only one proper subring.
PubDate: Thu, 14 Jul 2016 08:47:01 +000
- Spatial Tail Dependence and Survival Stability in a Class of Archimedean
Abstract: This paper investigates properties of extensions of tail dependence of Archimax copulas to high dimensional analysis in a spatialized framework. Specifically, we propose a characterization of bivariate margins of spatial Archimax processes while spatial multivariate upper and lower tail dependence coefficients are modeled, respectively, for Archimedean copulas and Archimax ones. A property of stability is given using convex transformations of survival copulas in a spatialized Archimedean family.
PubDate: Tue, 05 Jul 2016 06:39:02 +000
- On the Computation of Degenerate Hopf Bifurcations for -Dimensional
Multiparameter Vector Fields
Abstract: The restriction of an -dimensional nonlinear parametric system on the center manifold is treated via a new proper symbolic form and analytical expressions of the involved quantities are obtained as functions of the parameters by lengthy algebraic manipulations combined with computer assisted calculations. Normal forms regarding degenerate Hopf bifurcations up to codimension 3, as well as the corresponding Lyapunov coefficients and bifurcation portraits, can be easily computed for any system under consideration.
PubDate: Thu, 30 Jun 2016 11:31:33 +000
- On Shift-Dependent Cumulative Entropy Measures
Abstract: Measures of cumulative residual entropy (CRE) and cumulative entropy (CE) about predictability of failure time of a system have been introduced in the studies of reliability and life testing. In this paper, cumulative distribution and survival function are used to develop weighted forms of CRE and CE. These new measures are denominated as weighted cumulative residual entropy (WCRE) and weighted cumulative entropy (WCE) and the connections of these new measures with hazard and reversed hazard rates are assessed. These information-theoretic uncertainty measures are shift-dependent and various properties of these measures are studied, including their connections with CRE, CE, mean residual lifetime, and mean inactivity time. The notions of weighted mean residual lifetime (WMRL) and weighted mean inactivity time (WMIT) are defined. The connections of weighted cumulative uncertainties with WMRL and WMIT are used to calculate the cumulative entropies of some well-known distributions. The joint versions of WCE and WCRE are defined which have the additive properties similar to those of Shannon entropy for two independent random lifetimes. The upper boundaries of newly introduced measures and the effect of linear transformations on them are considered. Finally, empirical WCRE and WCE are proposed by virtue of sample mean, sample variance, and order statistics to estimate the new measures of uncertainty. The consistency of these estimators is studied under specific choices of distributions.
PubDate: Tue, 07 Jun 2016 06:02:35 +000
- Quantum Difference Langevin System with Nonlocal -Derivative Conditions
Abstract: We introduce a new class of boundary value problems for Langevin quantum difference systems. Some new existence and uniqueness results for coupled systems are obtained by using fixed point theorems. The existence and uniqueness of solutions are established by Banach’s contraction mapping principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. The obtained results are well illustrated with the aid of examples.
PubDate: Sun, 05 Jun 2016 14:33:02 +000
- More of Dedekind: His Series Test in Normed Spaces
Abstract: Dedekind’s test for infinite series has a canonical interpretation in the context of normed spaces. It is shown that his test holds in a normed space precisely when the space is complete.
PubDate: Tue, 31 May 2016 11:36:58 +000
- A Note on Primitivity of Ideals in Skew Polynomial Rings of Automorphism
Abstract: We extend results about primitive ideals in polynomial rings over nil rings originally proved by Smoktunowicz (2005) for -primitive ideals in skew polynomial rings of automorphism type.
PubDate: Mon, 30 May 2016 15:47:37 +000
- General Quadratic-Additive Type Functional Equation and Its Stability
Abstract: We investigate the general functional equation of the form − − , whose solutions are quadratic-additive mappings in connection with stability problems.
PubDate: Sun, 22 May 2016 06:21:26 +000
- The Agreement between the Generalized Value and Bayesian Evidence in the
One-Sided Testing Problem
Abstract: In the problem of testing one-sided hypotheses, a frequentist may measure evidence against the null hypothesis by the value, while a Bayesian may measure it by the posterior probability that the null hypothesis is true. In this paper, we consider the relationship between the generalized value and the Bayesian evidence in testing one-sided hypotheses in the presence of nuisance parameters. The sufficient conditions for the agreement between these two kinds of evidence are given. Some examples are provided to show the agreement of Bayesian and frequentist evidence in many classical testing problems. This is an illustration of reconcilability of evidence in a general framework where the nuisance parameters are present.
PubDate: Mon, 16 May 2016 11:54:31 +000
- A Tauberian Theorem for Double Cesàro Summability Method
Abstract: We have generalized Littlewood Tauberian theorems for summability of double sequences by using oscillating behavior and de la Vallée-Poussin mean. Further, the generalization of summability from summability is given as corollaries which were earlier established by the authors.
PubDate: Thu, 12 May 2016 17:15:35 +000