On multiplicative and Volterra minimization methods

Theory and applications of multiplicative and Volterra calculi have been evolving rapidly over the recent years. As numerical minimization methods have a wide range of applications in science and engineering, the idea of the design of minimization methods based on multiplicative and Volterra calculi is self-evident. In this paper, the well-known Newton minimization method for one and two variables is developed in the frameworks of multiplicative and Volterra calculi. The efficiency of these proposed minimization methods is exposed by examples, and the results are compared with the original minimization method. One of the striking results of the proposed method is that the rate of convergence and the range of initial values are considerably larger compared to the original method.     

A New Table of Binary/Ternary Mixed Covering Codes

A table of upper bounds for K3,2(n1,n2;R), the minimum number of codewords in a covering code with n1 ternary coordinates, n2 binary coordinates, and covering radius R, in the range n = n1 + n2 13, R 3, is presented. Explicit constructions of codes are given to prove the new bounds and verify old bounds. These binary/ternary covering codes can be used as systems for the football pool game. The results include a new binary code with covering radius 1 proving K2(13,1) 736, and the following upper bound for the football pool problem for 9 matches: K3(9,1) 1356.     

Stochastic independent modal-space control of distributed-parameter systems

A method is presented for solving time-varying independent modal-space Kalman filter equations in terms of 2×2 transition matrices, rather than in terms of the more commonly used 4×4 transition matrix solution technique. The basic method consists of replacing the well-known product form solution for the differential matrix Riccati equation with an alternate solution form which consists of a steady-state plus transient term.     

Compact-like operators in lattice-normed spaces

A linear operator $T$ between two lattice-normed spaces is said to be $p$-compact if, for any $p$-bounded net $x_{\alpha }$, the net $T{x}_{\alpha }$ has a $p$-convergent subnet. $p$-Compact operators generalize several known classes of operators such as compact, weakly compact, order weakly compact, $AM$-compact operators, etc. Similar to $M$-weakly and $L$-weakly compact operators, we define $p$-$M$-weakly and $p$-$L$-weakly compact operators and study some of their properties. We also study $up$-continuous and $up$-compact operators between lattice-normed vector lattices.     

A comparison study of fuzzy MADM methods in nuclear safeguards evaluation

Nuclear safeguards evaluation (NSE) is to verify that a State is living up to its international undertakings not to use nuclear programs for nuclear weapons purposes. The main issue in NSE is on the aggregation of expert evaluations for numerous indicators to make a final decision about the State’s nuclear activity. Fuzzy multiple attribute decision making (FMADM) methods are capable of dealing with such an issue. In this study, we propose a new FMADM methodology to solve the NSE problem. To this end, we investigate the applicability of four basic FMADM methods, namely a simple additive weighting method, a TOPSIS method, a linguistic method, and a non-compensatory method, to the NSE issue. As a result of the assessment of the basic methods, we propose a new FMADM methodology based on a new aggregation operator in which a cumulative belief structure is used to represent the expert evaluations. The basic methods and the proposed method as well are applied to an example from the literature for illustration purposes.     

On the neutrix convolution product ofx − r Inx − andx + −3

The existence of the neutrix convolution product of distributionx _? ^r Inx _? andx ₊ ^?3 is proved and some convolution products are evaluated.     

Oscillation analysis of neutral difference equations with delays

In this paper, we obtain some oscillation criteria for a class of neutral difference equations with time delays. We also investigate the behavior of the eventually positive solutions of these equations. To verify our results we give various numerical simulations by using the MATLAB programming.     

Elastoplastic stress analysis of thick laminated metal-matrix composite plates by the finite-element method

The elastoplastic stress state of a laminated stainless-steel-fiber-reinforced aluminum-matrix plates, with or without a hole, subjected to a pressure on their top is examined by using the finite-element method. The analysis is carried out for three layouts: (0/90/0/90)_s, (45/-45/45/-45)_s, and (30/60/30/60)_s. The Newton-Raphson method is used to solve the nonlinear problem. The distributions of equivalent stresses and the plastic zones of the plates without a hole and with a hole of various diameters are determined. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 531–544, July–August, 2006.     

Some Maximal Function Fields and Additive Polynomials

We derive explicit equations for the maximal function fields F over 𝔽 _{q ²ⁿ} given by F = 𝔽 _{q ²ⁿ} (X, Y) with the relation A(Y) = f(X), where A(Y) and f(X) are polynomials with coefficients in the finite field 𝔽 _{q ²ⁿ} , and where A(Y) is q-additive and deg(f) = q ⁿ  + 1. We prove in particular that such maximal function fields F are Galois subfields of the Hermitian function field H over 𝔽 _{q ²ⁿ} (i.e., the extension H/F is Galois).