We study the nonlinear energy diffusion through SYK chain in framework of Schwinger-Keldysh effective field theory. analytically construct interacting Lagrangian up to $40^{th}$ order derivative expansion. According this Lagrangian, we calculate first loop correction density response function, pole which is dispersion relation diffusion. As expected, see that standard expansion relation, $\omeg...

the right ventricle (rv) is a complex structure with abstruse function that reveals important differences when compared to the left ventricle (lv), so it cannot be described as a simple geometric form and achromatic physiology. as an inference from this fact, in the present review, we aim to describe rv structure including the embryology, anatomy, and physiology and present a functional, hemody...

The Faith-Menal conjecture says that every strongly right Johns ring is QF . The conjecture is also equivalent to say every right noetherian left FP -injective ring is QF . In this short article, we show that the conjecture is true under the condition( a proper generalization of left CS condition) that every nonzero complement left ideal is not small( a left ideal I is called small if for every...

We give exact formulas for the right-handed analog of the Cabibbo-Kobayashi-Maskawa (CKM) matrix in the minimal left-right symmetric theory, for the case when the left-right symmetry is generalized parity as in the original version of the theory. We derive its explicit form and give a physical reason for the known and surprising fact that the right-handed mixing angles are close to the CKM ones...

We obtain uniqueness and existence of a solution u to the following second-order stochastic partial differential equation: 1 $$\begin{aligned} du= \left( {\bar{a}}^{ij}(\omega ,t)u_{x^ix^j}+ f \right) dt + g^k dw^k_t, \quad t \in (0,T); u(0,\cdot )=0, \end{aligned}$$ where $$T (0,\infty )$$ , $$w^k$$ $$(k=1,2,\ldots are independent Wiener processes, $$({\bar{a}}^{ij}(\omega ,t))$$ is (predictab...

Let R be a left and right Noetherian ring and n, k any non-negative integers. R is said to satisfy the Auslander-type condition Gn(k) if the right flat dimension of the (i+1)-st term in a minimal injective resolution of RR is at most i+ k for any 0 ≤ i ≤ n− 1. In this paper, we prove that R is Gn(k) if and only if so is a lower triangular matrix ring of any degree t over R.

‎The ABS methods‎, ‎introduced by Abaffy‎, ‎Broyden and Spedicato‎, ‎are‎‎direct iteration methods for solving a linear system where the‎‎$i$-th iteration satisfies the first $i$ equations‎, ‎therefore a‎ ‎system of $m$ equations is solved in at most $m$ steps‎. ‎In this‎‎paper‎, ‎we introduce a class of ABS-type methods for solving a full row‎‎rank linear equations‎, ‎w...

Let k ⊆ L be division rings, with [L : k ]right < ∞, and let Bk ⊆ AL be right vector spaces. Conditions are established in terms of the k-codimension of B in A, respectively the k-dimension of B, for there to exist a nonzero element a ∈A such that aL ∩ B = {0}, respectively an L-linear functional f on A such that f (B) = L . Some consequences and related open questions are discussed. Suppose k ...

In 1967, Grünbaum conjectured that any d-dimensional polytope with d + s ? 2d vertices has at least $${\phi _k}(d s,d) = \left( {\matrix{{d 1} \cr {k } \right) {\matrix{d - {\matrix{ {d 1 s} \right)$$ k-faces. We prove this conjecture and also characterize the cases in which equality holds.