Some paranormed sequence spaces of non-absolute type derived by weighted mean

The sequence spaces ?_∞(p), c(p) and c₀(p) were introduced and studied by Maddox [I.J. Maddox, Paranormed sequence spaces generated by infinite matrices, Proc. Cambridge Philos. Soc. 64 (1968) 335-340]. In the present paper, the sequence spaces λ(u,v;p) of non-absolute type which are derived by the generalized weighted mean are defined and proved that the spaces λ(u,v;p) and λ(p) are linearly isomorphic, where λ denotes the one of the sequence spaces ?_∞, c or c₀. Besides this, the β- and γ-duals of the spaces λ(u,v;p) are computed and the basis of the spaces c₀(u,v;p) and c(u,v;p) is constructed. Additionally, it is established that the sequence space c₀(u,v) has AD property and given the f-dual of the space c₀(u,v;p). Finally, the matrix mappings from the sequence spaces λ(u,v;p) to the sequence space μ and from the sequence space μ to the sequence spaces λ(u,v;p) are characterized.     

The consistent Mindlin’s thermopiezoelectric equations and the principle of virtual work

The thermal field vector, an overlooked concept of importance, is introduced for the consistency in Mindlin’s thermopiezoelectric equations. The gradient of the temperature increment is defined as the thermal field vector; an analogous to the electric and magnetic field vectors (i.e., the gradients of the electric and magnetic potentials). The thermal field vector is used to state the universal gradient equations, and then, the principle of virtual work.     

Some new spaces of double sequences

In this study, we define the double sequence spaces BS, BS(t), CSp, CSbp, CSr and BV, and also examine some properties of those sequence spaces. Furthermore, we show that these sequence spaces are complete paranormed or normed spaces under some certain conditions. We determine the α-duals of the spaces BS, BV, CSbp and the β(?)-duals of the spaces CSbp and CSr of double series. Finally, we give the conditions which characterize the class of four-dimensional matrix mappings defined on the spaces CSbp, CSr and CSp of double series.     

Characterizing CA2 and CA6 using ELNES

Calcium aluminates, compounds in the CaO-Al₂O₃ phase system, are used in high-temperature cements and refractory oxides and have wide range of potential technological applications due to their interesting optical, electrical, thermal, and mechanical properties. They are used in both crystalline and glassy form; the glass is an isotropic material while the crystalline materials may be highly anisotropic. This paper will consider two particular crystalline materials, CA₂ and CA₆, but the results should be applicable to all calcium aluminates. Although CA₂ and CA₆ crystals contain the same chemical species, Ca, Al, and O, the coordination and local environments of these species are different in the two structures and hence they show very different energy-loss near-edge structures (ELNES) when examined by electron energy-loss spectroscopy (EELS) in the TEM. The data obtained using ELNES can effectively provide a fingerprint for each compound and a map for their electronic structure. Once such fingerprints are obtained, they can be used to identify nano-sized particles/grains or material at interfaces and grain boundaries.In the present study, the local symmetry fingerprints for CA₂ and CA₆ structures are reported combining experimental spectra with electronic-structure calculations that allow the different features in the spectra to be interpreted. Al-L_2,3 and O-K edge core-loss spectra from CA₂ and CA₆ were measured experimentally using electron energy-loss spectroscopy in a monochromated scanning transmission electron microscope. The near-edge structures were calculated for the different phases using the orthogonalized linear combination of atomic-orbitals method, and took account of core-hole interactions. It is shown that CA₂ and CA₆ structures exhibit distinctive experimental ELNES fingerprints so that these two phases can be separately identified even when present in small volumes.     

Approximate period calculation for some strongly nonlinear oscillation by He’s parameter-expanding methods

In this paper, He’s modified Lindstedt–Poincare method and bookkeeping parameter method, also known as He’s parameter-expanding method, is applied to various kinds of strongly nonlinear oscillators. We obtained sufficiently accurate solutions with one iteration which is valid for whole domain to the contrary of classical perturbation techniques.     

Exact and heuristic solution approaches for the mixed integer setup knapsack problem

We consider a class of knapsack problems that include setup costs for families of items. An individual item can be loaded into the knapsack only if a setup cost is incurred for the family to which it belongs. A mixed integer programming formulation for the problem is provided along with exact and heuristic solution methods. The exact algorithm uses cross decomposition. The proposed heuristic gives fast and tight bounds. In addition, a Benders decomposition algorithm is presented to solve the continuous relaxation of the problem. This method for solving the continuous relaxation can be used to improve the performance of a branch and bound algorithm for solving the integer problem. Computational performance of the algorithms are reported and compared to CPLEX.     

Certain topological properties and duals of the domain of a triangle matrix in a sequence space

The matrix domain of the particular limitation methods Cesàro, Riesz, difference, summation and Euler were studied by several authors. In the present paper, certain topological properties and β- and γ-duals of the domain of a triangle matrix in a sequence space have been examined as an application of the characterization of the related matrix classes.