A new class of symmetric (v,k, λ)-designs

We construct new families of symmetric (v, k, )-designs with parameters

Cyclic homology of K[?/p·?]

The cyclic homology of the group algebra A= K[G] for a finite cyclic group G=Z/pZ and p a prime not a zero divisor in K, is

Microwave spectra and centrifugal distortion constants of orthofluoropyridine

The microwave spectra of orthofluoropyridine due to high J transitions has been analysed in order to determine its centrifugal distortion constants. The final values of rotational and centrifugal distortion constants are: $$\begin{gathered} A = 5870 \cdot 856 \pm 0 \cdot 011 MHz \tau _{aaaa} = - 2 \cdot 46_5 \pm 0 \cdot 016 KHz \hfill \\ B = 2699 \cdot 971 \pm 0 \cdot 005 MHz \tau _{bbbb} = - 0 \cdot 42_2 \pm 0 \cdot 003 KHz \hfill \\ C = 1849 \cdot 244 \pm 0 \cdot 004 MHz \tau _{cccc} = - 0 \cdot 0 (fixed) KHz \hfill \\ \tau _{abab} = - 0 \cdot 61_8 \pm 0 \cdot 015 KHz \hfill \\ \end{gathered} $$ Using these constants a number of transitions have been assigned upto J = 60.     

Small prime solutions of some additive equations

Essentially sharp bounds for small prime solutionsp _j ,q _i of the following two different types of equations are obtained.

Some approximation theorems for modified Bernstein-Durrmeyer operators

The modified Bernstein-Durrmeyer operators discussed in this paper are given byM_nf≡M_n(f,x)=(n+2)P_(n,k)∫_0~1p_n+1.k(t)f(t)dt,whereWe will show,for 0<α<1 and 1≤p≤∞     

Combinatorial identity obtained by the differentiation of convolution

The combinatorial identity

Fourier-integral-operator product representation of solutions to first-order symmetrizable hyperbolic systems

We consider the first-order Cauchy problem

A Problem with Nonlocal Boundary Conditions for a Quasilinear Parabolic Equation

The solvability of the nonlocal boundary value problem

Determinantal Inequalities for Accretive-Dissipative Matrices

A matrix is said to be accretive-dissipative if, in its Hermitian decomposition , both matrices B and C are positive definite. Further, if B= I _n, then A is called a Buckley matrix. The following extension of the classical Fischer inequality for Hermitian positive-definite matrices is proved. Let be an accretive-dissipative matrix, k and l be the orders of A ₁₁ and A ₂₂, respectively, and let m = min{k,l}. Then For Buckley matrices, the stronger bound is obtained. Bibliography: 5 titles.     

Properties of kagi and renko moments for homogeneous diffusion processes

For a homogeneous diffusion process (X _t ) _t?0, we consider problems related to the distribution of the stopping times $\begin{gathered} \gamma _{\max } = \inf \{ t \geqslant 0:\mathop {\sup }\limits_{s \leqslant t} X_s - X_t \geqslant H\} ,\gamma _{\min } = \inf \{ t \geqslant 0:X_t - \mathop {\inf }\limits_{s \leqslant t} X_s \geqslant H\} , \hfill \\ \kappa _0 = \inf \{ t \geqslant 0:\mathop {\sup }\limits_{s \leqslant t} X_s - \mathop {\inf }\limits_{s \leqslant t} X_s \geqslant H\} . \hfill \\ \end{gathered} $ . The results obtained are used to construct an inductive procedure allowing us to find the distribution of the increments of the process X between two adjacent kagi and renko instants of time.     

Diameter of the set of midpoints of chords of a bounded closed set

The estimate is obtained for the diameter d(S_n(a)) of the set S_n(a) of midpoints of chords of length ≥a(0n, namely $$d(S_n (a)) \leqslant \left\{ \begin{gathered} 1 - a^2 /2, n = 2, \hfill \\ \sqrt {1 - a^2 /2,} n \geqslant 3, \hfill \\ \end{gathered} \right.$$ and it is shown that the inequality cannot be improved.     

Rank formulae for factorized groups

The following inequalities for the torsion-free rank r₀(G) of the group G=AB and for the p^∞-rank r_p(G) of the soluble-by-finite group G=AB are stated: $$\begin{gathered} r_0 (G) \leqslant r_0 (A) + r_0 (B) - r_0 (A \cap B), \hfill \\ r_p (G) \leqslant r_p (A) + r_p (B) - r_p (A \cap B). \hfill \\ \end{gathered} $$      

On a Class of Infinite-Dimensional Hamiltonian Systems with Asymptotically Periodic Nonlinearities

The authors study the existence of homoclinic type solutions for the following system of diffusion equations on R × RN:{■tu-xu + b ·▽xu + au + V(t,x)v = Hv(t,x,u,v),-■tv-xv-b·▽xv + av + V(t,x)u = Hu(t,x,u,v),where z =(u,v):R × RN → Rm × Rm,a > 0,b =(b1,···,bN) is a constant vector and V ∈ C(R × RN,R),H ∈ C1(R × RN × R2m,R).Under suitable conditions on V(t,x) and the nonlinearity for H(t,x,z),at least one non-stationary homoclinic solution with least energy is obtained.     

Uniform meyer solution to the three dimensional cauchy problem for laplace equation

We consider the three dimensional Cauchy problem for the Laplace equation uxx(x,y,z)+ uyy(x,y,z)+ uzz(x,y,z) = 0, x ∈ R,y ∈ R,0 z ≤ 1, u(x,y,0) = g(x,y), x ∈ R,y ∈ R, uz(x,y,0) = 0, x ∈ R,y ∈ R, where the data is given at z = 0 and a solution is sought in the region x,y ∈ R,0 z 1. The problem is ill-posed, the solution (if it exists) doesn't depend continuously on the initial data. Using Galerkin method and Meyer wavelets, we get the uniform stable wavelet approximate solution. Furthermore, we shall give a recipe for choosing the coarse level resolution.     

Structures and uniqueness conditions of MK-weighted pseudoinverses

For given matricesM, A andK of appropriate sizes, we study the following two kinds of MK-weighted pseudoinverses ofA. The first kind of weighted pseudoinverseX is characterized by the following four Moore-Penrose like conditions:

An estimate of an incomplete linear form in several algebraic numbers

Letμ>m?1, letν be a rational number, and letω _k=b _k ^v , where b_k ≠ 0 are distinct numbers of an imaginary quadratic field K, which satisfy some additional conditions. Then $$\begin{gathered} |{}_1x_1 \omega _1 + ... + x_m \omega _m | > X^{ - \mu } , \hfill \\ X = \max |x_k | \geqslant X, > 0, \hfill \\ 1 \leqslant k \leqslant m \hfill \\ \end{gathered}$$ where x₁, ..., x_m are integers of the field K, and X₀ is an effective constant.     

The critical exponent for a weakly coupled system of the generalized Fujita type reaction-diffusion equations

We study nonnegative solutions of the initial value problem for a weakly coupled system

THE BEST APPROXIMATION CONSTANT FOR THE JACKSON''''S TYPE OPERATOR J_(n,3) (f;x)

In this paper we obtain the best approximation constant of function f(x)(∈C_(2π))by theJackson's type operator J_(π3)(f;x),i.e.‖J_(n,3)(f,x)-f(x)‖_c≤(4-6/π)ω(f,1/n),‖J_(n,3)(f,x)-f(x)‖_c≤(8-17/π)ω_2(f,1/n)     

Best quadrature formula on the class W * r L2 of periodic functions

For the classes of periodic functions with r-th derivative integrable in the mean,we obtain a best quadrature formula of the form $$\begin{gathered} \int_0^1 {f(x)dx = \sum\nolimits_{k = 0}^{m - 1} {\sum\nolimits_{l = 0}^\rho {p_{k,l} } } } f^{(l)} (x_k ) + R(f),0 \leqslant \rho \leqslant r - 1, \hfill \\ 0 \leqslant x_0< x_1< ...< x_{m - 1} \leqslant 1, \hfill \\ \end{gathered}$$ where ρ=r?2 and r?3, r=3, 5, 7, ..., and we determine an exact bound for the error of this formula.     

Isotope shifts in the second negative bands of O 2 +

The second negative bands of O ₂ ⁺ , lying in the region 5000–1850 Å, have been photographed using oxygen enriched in¹⁸O. A study of the isotope shifts in the band heads revealed that thev″ numbering is to be increased by one unit whereas thev′ numbering remains unaltered. This change in vibrational numbering leads to a revision of the molecular constants of O ₂ ⁺ , especially of those in its ground state. These are discussed and the extension of the band system in the vacuum ultra-violet region reported. The possibility of developing a simple spectrographic method for the isotopic assay of oxygen using the isotope shifts in this band system is pointed out. The revised rotational and vibrational constants in theX ² II _g ground state of O ₂ ⁺ molecule are as follows :

$$\begin{gathered} \omega _e = 1903 \cdot 85 cm.^{ - 1} , \hfill \\ \omega _e x_e = 16 \cdot 18 cm.^{ - 1} , \hfill \\ B_e = 1 \cdot 6920 cm.^{ - 1} \hfill \\ and \hfill \\ r_e = 1 \cdot 1161 {\AA}. \hfill \\ \end{gathered} $$