in this paper, we use a third degree b-spline function to construct an approximate solution forthird order linear and nonlinear boundary value problems coupled with the least square method. severalexamples are given to illustrate the efficiency of the proposed technique.

The l-1 norm based optimization is widely used in signal processing, especially in recent compressed sensing theory. This paper studies the solution path of the l-1 norm penalized least-square problem, whose constrained form is known as Least Absolute Shrinkage and Selection Operator (LASSO). A solution path is the set of all the optimizers with respect to the evolution of the hyperparameter (L...

Felice Russo 1vIicrolZ Technology ltal)/ Avezzano (Aq) ItaZv In this not~ we r~port the solution of an unsolved qu~stion on Smarandache Squar~-Partial-Digital Subsequ~nce. We have found it by ~xtesi\'~ computer search. Some n~w questions about palindromic numb~rs and prime numbers in SSPDS are posed too. Introduction The Smarandache Square-Partial-Digital Subsequence (SSPDS) is the sequenc~ of ...

Observational evidence indicates that the bubble layer beneath the sea surface may show either an exponential or an inverse-square sound speed profile down to depths greater than 10 m. An exponential profile is consistent with a model of gas transport in which the downwardflux is due to turbulent diffusion and the d@usion coeficient is independent of depth. In this paper, a theoretical model is...

The arctic circle theorem of Jockusch, Propp, and Shor asserts that uniformly random domino tilings of an Aztec diamond of high order are frozen with asymptotically high probability outside the “arctic circle” inscribed within the diamond. A similar arctic circle phenomenon has been observed in the limiting behavior of random square Young tableaux. In this paper, we show that random domino tili...

After a survey of some known lattice results, we determine the greatest idempotent (resp. compact) solution, when it exists, of a finite square rational equation assigned over a linear lattice. Similar considerations are presented for composite relational equations.

In this paper, we present a novel approach of implementing a combination methodology to find appropriate neural network architecture and weights using an evolutionary least square based algorithm (GALS).1 This paper focuses on aspects such as the heuristics of updating weights using an evolutionary least square based algorithm, finding the number of hidden neurons for a two layer feed forward n...

The general form of the Smoluchowski equation in two reaction coordinates is obtained as the diffusion limit of a random walk on an infinite square grid using transition probabilities that satisfy detailed balance at thermodynamic equilibrium. The diffusion limit is then used to construct a generalization of the single-particle model to two reaction coordinates. The state space includes a squar...

There are many practical applications based on the Least Square Error (LSE) or Total Least Square Error (TLSE) methods. Usually the standard least square error is used due to its simplicity, but it is not an optimal solution, as it does not optimize distance, but square of a distance. The TLSE method, respecting the orthogonality of a distance measurement, is computed in -dimensional space, i.e...

In this paper we study the problem of deciding whether a given compressed string contains a square. A string x is called a square if x = zz and z = uk implies k = 1 and u = z. A string w is said to be square-free if no substrings of w are squares. However, very little is known for testing square-freeness of a given compressed string. In this paper, we give an O(max(n2,n log2 N))-time O(n2)-spac...