AbstractWe have classified symmetric solutions around the origin to four dimensional degenerate Painleve type equation NYA4 with generic values of parameters. We obtained sixteen meromorphic solutions, which are transformed each other by Backlund transformation. calculated linear monodromy for one them, explicitly.

This paper concerns the function S(t), the argument of the Riemann zeta-function along the critical line. Improving on the method of Backlund, and taking into account the refinements of Rosser and McCurley it is proved that for sufficiently large t |S(t)| ≤ 0.1013 log t. Theorem 2 makes the above result explicit, viz. it enables one to select values of a and b such that, for t > t0, |S(t)| ≤ a+...

This paper concerns the function S(T ), the argument of the Riemann zeta-function. Improving on the method of Backlund, and taking into account the refinements of Rosser and McCurley it is hereunder proved that for sufficiently large T |S(T )| ≤ 0.1013 log T. Theorem 2 makes the above result explicit, viz. it enables one to select values of a and b such that, for T > T0, |S(T )| ≤ a + b log T.

For each quadratic form $$Q\in \text{ Quad }(V)$$ on a vector space over field $$\mathbb {K},$$ we can define the Clifford algebra $${{\,\textrm{Cl}\,}}(V,Q)$$ as quotient $${{\,\textrm{T}\,}}(V)/I(Q)$$ of tensor $${{\,\textrm{T}\,}}(V)$$ by two-sided ideal generated expressions $$x\otimes x-Q(x),\, x\in V.$$ In present paper consider whole family $$\{{{\,\textrm{Cl}\,}}(V,Q):\, Q\in }(V)\}$$ i...

Gated networks are that contain gating connections in which the output of at least two neurons multiplied. The basic idea a gated restricted Boltzmann machine (RBM) model is to use binary hidden units learn conditional distribution one image (the output) given another input). This allows RBM transformations between successive images. Inference consists extracting pair However, fully connected m...

objective: in this study, we aimed to validate the accuracy of computed tomography-based attenuation correction (ctac) using the bilinear scaling method.methods: the measured attenuation coefficient (μm) was compared to a theoretical attenuation coefficient (μt ) using four different ct scanners and an rmi 467 phantom. the effective energy of the ct beam x-rays was calculated, using the aluminu...