The renormalization group (RG) method is one of the singular perturbation methods which is used in search for asymptotic behavior of solutions of differential equations. In this article, time-independent vector fields and time (almost) periodic vector fields are considered. Theorems on error estimates for approximate solutions, existence of approximate invariant manifolds and their stability, i...

Judging by the increasing impact of machine learning on large-scale data analysis in the last decade, one can anticipate a substantial growth in diversity of the machine learning applications for “big data” over the next decade. This exciting new opportunity, however, also raises many challenges. One of them is scaling inference within and training of graphical models. Typical ways to address t...

A quantum compiling algorithm is an algorithm for decomposing (“compiling”) an arbitrary unitary matrix into a sequence of elementary operations (SEO). Suppose Uin is an NB-bit unstructured unitary matrix (a unitary matrix with no special symmetries) that we wish to compile. For NB > 10, expressing Uin as a SEO requires more than a million CNOTs. This calls for a method for finding a unitary ma...

Generalization abilities of empirical learning systems are essentially based on a priori information. The paper emphasizes the need of empirical measurement of a priori information by a posteriori control. A priori information is treated analogously to an infinite number of training data and expressed explicitly in terms of the function values of interest. This contrasts an implicit implementat...

In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second ...

In this paper, symmetry properties of the basic equations atmospheric motion are proposed. The results on symmetries show that invariant under space-time translation transformation, Galilean transformations and scaling transformations. Eight one-parameter subgroups eight group solutions demonstrated. Three types nontrivial similarity invariants With help perturbation method, we derive second-or...

we study the notion of bounded approximate connes-amenability for‎ ‎dual banach algebras and characterize this type of algebras in terms‎ ‎of approximate diagonals‎. ‎we show that bounded approximate‎ ‎connes-amenability of dual banach algebras forces them to be unital‎. ‎for a separable dual banach algebra‎, ‎we prove that bounded‎ ‎approximate connes-amenability implies sequential approximate...

The smallness of fermion masses and mixing angles has recently been been attributed to approximate global U(1) symmetries, one for each fermion type. The parameters associated with these symmetry breakings are estimated here directly from observed masses and mixing angles. It turns out that although flavor changing reaction rates may be acceptably small in electroweak theories with several scal...

Generalization abilities of empirical learning systems are essentially based on a priori information. The paper emphasizes the need of empirical measurement of a priori information by a posteriori control. A priori information is treated analogously to an infinite number of training data and expressed explicitly in terms of the function values of interest. This contrasts an implicit implementat...

The approximate conservation of CP can be naturally understood if it arises as an automatic symmetry of the renormalizable Lagrangian. We present a specific realistic example with this feature. In this example, the global Peccei-Quinn symmetry and gauge symmetries of the model make the renormalizable Lagrangian CP invariant but allow non zero hierarchical masses and mixing among the three gener...