in this paper, an efficient method for solving optimal control problemsof the linear differential systems with inequality constraint is proposed. by usingnew adjustment of hat basis functions and their operational matrices of integration,optimal control problem is reduced to an optimization problem. also, the erroranalysis of the proposed method is investigated and it is proved that the order o...

‎It is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎For‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎This paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎The fractional derivatives are described...

We analyze the notion of guessing model, a way to assign combinatorial properties to arbitrary regular cardinals. Guessing models can be used, in combination with inaccessibility, to characterize various large cardinals axioms, ranging from supercompactness to rank-to-rank embeddings. The majority of these large cardinals properties can be defined in terms of suitable elementary embeddings j : ...

We say that κ is μ-hypermeasurable (or μ-strong) for a cardinal μ ≥ κ+ if there is an embedding j : V → M with critical point κ such that H(μ)V is included in M and j(κ) > μ. Such j is called a witnessing embedding. Building on the results in [7], we will show that if V satisfies GCH and F is an Easton function from the regular cardinals into cardinals satisfying some mild restrictions, then th...

Consider the set D[a,b] of all cumulative distribution functions F(·) over some interval [a,b], and an individual whose preference ranking over this set can be represented by a real-valued preference functional V(F), in the sense that the distribution F*(·) is weakly preferred to F(·) if and only if V(F*) ≥ V(F). Note that V(·) is ordinal in the sense that some other functional V*(·) will repre...

Every m th order cardinal spline wavelet is a linear combination of the functions fN (l) m+l (2x?j); j 2 Zg. Here the function N m is the m th order cardinal B-spline. In this paper we prove that the single function N (l) m+l (2x), or N (l) m+l (2x ? 1) is a wavelet when m and l satisfy some mild conditions. As l decreases, so does the support of the wavelet. When l increases, the smoothness of...

For Tychonoff X and α an infinite cardinal, let αdef X := the minimum number of α cozero-sets of the Čech-Stone compactification which intersect to X (generalizing R-defect), and let rtX := minα max(α, α def X). Give C(X) the compact-open topology. It is shown that τC(X) ≤ nχC(X) ≤ rtX = max(L(X), L(X) def X), where: τ is tightness; nχ is the network character; L(X) is the Lindelöf number. For ...

We establish a new Easton theorem for the least supercompact cardinal κ that is consistent with the level by level equivalence between strong compactness and supercompactness. This theorem is true in any model of ZFC containing at least one supercompact cardinal, regardless if level by level equivalence holds. Unlike previous Easton theorems for supercompactness, there are no limits on the East...

In the present paper, a numerical method is considered for solving one-dimensional heat equation subject to both Neumann and Dirichlet initial boundary conditions. This method is a combination of collocation method and radial basis functions (RBFs). The operational matrix of derivative for Laguerre-Gaussians (LG) radial basis functions is used to reduce the problem to a set of algebraic equatio...