The problem we are dealing with is the following: find two sequences an and bn such that the average of the first bn triangular numbers (starting with the triangular number 1) is still a triangular number, precisely the an-th triangular number. We get also some side results: for instance one of the sequence instrumental to finding the asked for sequences turns out to be a bisection of the seque...

Ext ∞ 2 +• A (C, ·) was given. The setup for the definition of semiinfinite cohomology of an algebra A includes two subalgebras B,N ⊂ A and the triangular decomposition of A, i. e. the vector space isomorphism B⊗N−̃→A provided by the multiplication in A. Fix root data (Y,X, . . . ) of the finite type (I, ·) and a positive integer number l. The small quantum group ul with the standard triangular ...

Through introducing two piecewise-linear triangular wave functions in a three-dimensional spiral chaotic Colpitts oscillator model, a four-dimensional grid multiscroll hyperchaotic system is constructed. Interestingly, by adjusting a build-in parameter in a variable of one triangle wave function, the control of the gradient of the multiscroll grid is achieved. Whereas by deploying the zero poin...

Classical extreme value theory for stationary sequences of random variables can to a large extent be paraphrased as the study of exceedances over a high threshold. A special role within the description of the temporal dependence between such exceedances is played by the extremal index. Parts of this theory can be generalized not only to random variables on an arbitrary state space hitting certa...

we survey some recent results on cocharacters of upper triangular matrices. in particular, we deal both with ordinary and graded cocharacter sequence; we list the principal combinatorial results; we show di erent tech-niques in order to solve similar problems.

The nonlinear scalar-field realisation of w 1+∞ symmetry in d = 2 dimensions is studied in analogy to the nonlinear realisation of d = 4 conformal symmetry SO(4, 2). The w 1+∞ realisation is derived from a coset-space construction in which the divisor group is generated by the non-negative modes of the Virasoro algebra, with subsequent application of an infinite set of co-variant constraints. T...

Studies of three–dimensional and two–dimensional condensed phases have shown that many– body interactions contribute ∼ 10% to the equations of state of noble gases. This paper assesses the importance of three–body triple dipole interactions for quasi–one–dimensional phases of He, Ne, H2, Ar, Kr and Xe confined within interstitial channels or on the external surfaces of nanotube bundles. We find...

Ab initio electronic structure calculations on several low-lying valence states of B, have been carried out using correlation-consistent polarized valence double-zeta basis sets and completeactive-space self-consistent field treatments of electron correlation. Stable triangular structures, linear structures, and Jahn-Teller unstable structures are all observed. Equilibrium geometries, energies,...

We study two-dimensional triangular-network models, which have degenerate ground states composed of straight or randomly-zigzagging stripes and thus sub-extensive residual entropy. We show that attraction is responsible for the inversion of the stable phase by changing the entropy of fluctuations around the ground-state configurations. By using a real-space shell-expansion method, we compute th...