Abstract In this work, we prove a version of the Sylvester–Gallai theorem for quadratic polynomials that takes us one step closer to obtaining deterministic polynomial time algorithm testing zeroness $\Sigma ^{[3]}\Pi \Sigma \Pi ^{[2]}$ circuits. Specifically, that, if finite set irreducible ${\mathcal {Q}}$ satisfies every two $Q_1,Q_2\in {\mathcal there is subset {K}}\subset such $Q_1,Q_2 \no...

Investigated in this paper are the uniform approximation capabilities of sum-of-product (SOPNN) and sigma-pi-sigma (SPSNN) neural networks. It is proved that the set of functions that are generated by an SOPNN with its activation function in C(R) is dense in C(K) for any compact K ∈ R , if and only if the activation function is not a polynomial. It is also shown that if the activation function ...

Abstract Given a point w in the open upper complex half-plane $$\Pi _{\mathord {+}}$$ Π + , we describe set of possible values $$F_\sigma \left( {w}\right) $$ F σ w St...

We present a process semantics for the purely additive fragment of linear logic in which formulas denote protocols and (equivalence classes of) proofs denote multichannel concurrent processes. The polycategorical model induced by this process semantics is shown to be equivalent to the free polycategory based on the syntax (i.e., it is full and faithfully complete). This establishes that the add...

In heavy ion reactions at energies around (1-2)A GeV the measured K- yields appear rather high as compared to pp collisions as shown by the KaoS Collaboration. Employing quantum molecular dy-namics simulations, we show that this is caused by the fact that the dominant production channel is not BB-->BBK+K- but the mesonic Lambda(Sigma)pi-->K-B reaction. Because the Lambda (Sigma) stem from the r...

Based on a sample of 4.4 $\mathrm{fb}^{-1}$ $e^{+}e^{-}$ annihilation data collected in the energy region between 4.6 GeV and 4.7 with BESIII detector at BEPCII, two singly Cabibbo-suppressed decays $\Lambda_c^+ \rightarrow \Sigma^0 K^+$ $\Lambda_{c}^{+} \Sigma^+ K_{S}^0$ are studied. The ratio branching fraction $\mathcal{B}(\Lambda_c^+ K^+)$ relative to \pi^+)$ is measured be $0.0361 \pm 0.00...

Twenty-three diarylcarbenium ions and 38 pi-systems (arenes, alkenes, allyl silanes and stannanes, silyl enol ethers, silyl ketene acetals, and enamines) have been defined as basis sets for establishing general reactivity scales for electrophiles and nucleophiles. The rate constants of 209 combinations of these benzhydrylium ions and pi-nucleophiles, 85 of which are first presented in this arti...

In this paper the Sigma-if artificial neural network model is considered, which is a generalization of an MLP network with sigmoidal neurons. It was found to be a potentially universal tool for automatic creation of distributed classification and selective attention systems. To overcome the high nonlinearity of the aggregation function of Sigma-if neurons, the training process of the Sigma-if n...

Cultured cerebellar granule neurons die by apoptosis when switched from a medium containing an elevated level of potassium (K+) to one with lower K+ (5 mM). Death resulting from the lowering of K+ can be prevented by insulin-like growth factor (IGF-1). To understand how IGF-1 inhibits apoptosis and maintains neuronal survival, we examined the role of phosphoinositide 3-kinase (PI 3-kinase). Act...

Metal-thiolate active sites play major roles in bioinorganic chemistry. The M--S(thiolate) bonds can be very covalent, and involve different orbital interactions. Spectroscopic features of these active sites (intense, low-energy charge transfer transitions) reflect the high covalency of the M--S(thiolate) bonds. The energy of the metal-thiolate bond is fairly insensitive to its ionic/covalent a...