This is a short review of the Kadomtsev–Petviashvili hierarchies types $$\mathrm{B}$$ and $$\mathrm{C}$$ . The main objects are $$L$$ operator, wave auxiliary linear problems for function, bilinear identity tau function. All them discussed in paper. Connections with usual (type- $$\mathrm{A}$$ ) hierarchy clarified. Examples soliton solutions dispersionless limit also considered.

Frontotemporal dementia (FTD) is a clinical syndrome with a heterogeneous molecular basis. Familial FTD has been linked to mutations in several genes, including those encoding the microtubule-associated protein tau (MAPT), progranulin (GRN), valosin-containing protein (VCP) and charged multivescicular body protein 2B (CHMP2B). The associated neuropathology is characterised by selective degenera...

‎In this paper‎, ‎we define and study the notion of zero elements in topoframes; a topoframe is a pair‎ ‎$(L‎, ‎tau)$‎, ‎abbreviated $L_{ tau}$‎, ‎consisting of a frame $L$ and a‎ ‎subframe $ tau $ all of whose elements are complemented elements in‎ ‎$L$‎. ‎We show that‎ ‎the $f$-ring $ mathcal{R}(L_tau)$‎, ‎the set of $tau$-real continuous functions on $L$‎, ‎is uniformly complete‎. ‎Also‎, ‎t...

In this paper, we study monotone set functions defined as the composition of an additive measure with a strictly increasing function. This function is unary operator in continuous-valued logic, called tau function, and it generator function-based parametric mapping. We provide necessary sufficient condition for equality two that are induced by different functions. Using its properties, introduc...

The excited-state quenching of zinc meso-tetrakis(4-sulfonatophenyl)porphyrin (ZnTPPS) by halide ions has been studied in water and various aqueous micellar solutions using both steady-state and time-resolved fluorescence techniques. The quenching efficiencies of the S(1) state of ZnTPPS ([small tau][approximate] 1.93 ns) by halide ions in homogeneous aqueous solution increase in the order Cl(-...

In this paper, numerical technique based on monic Laguerre polynomials is proposed to obtain approximate solutions of initial value problems for systems fractional order integro-differential equations (FIDEs). Operational integral matrix constructed. This operational applied together with the Tau method solve FIDEs. FIDEs will be transformed into a system algebraic which can solved easily. Nume...

In this paper we address the problem of the numerical integration of the time-dependent Schrodinger equation i partial differential (t)phi=Hphi. In particular, we are concerned with the important case where H is the self-consistent Kohn-Sham Hamiltonian that stems from time-dependent functional theory. As the Kohn-Sham potential depends parametrically on the time-dependent density, H is in gene...

Biochemical reaction networks are often modelled using discrete-state, continuoustime Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie’s di...

In large data recording and warehousing environments it is often advantageous to provide fast approximate answers to queries whenever possible The goal is to provide an estimated response in orders of magnitude less time than the time to compute an exact answer by avoiding or minimizing the number of accesses to the base data This white paper describes the Approximate QUery Answering AQUA Proje...