We describe the structure of coefficient ring $$W^*(pt)=\varOmega_W^*$$ $$c_1$$ -spherical bordism theory for an arbitrary $$SU$$ -bilinear multiplication. prove that any multiplication formal group $$W^*$$ is Landweber exact. Also we show after inverting set $$\mathcal{P}$$ Fermat primes there exists a complex orientation localized $$W^*[\mathcal{P}^{-1}]$$ such coefficients corresponding law ...

We consider a general 3-dimensional Lotka-Volterra system with rational first integral of degree two the form \(H=x^i y^j z^k\). The restriction this to each surface \(H(x,y,z)=h\) varying \(h\in \mathbb{R}\) provide Kolmogorov systems. With additional assumption that they have Darboux invariant \(x^\ell y^m e^{st}\) reduce systems $$\displaylines{ \dot{x}=x\big(a_0- \mu (c_1 x + c_2 z^2 c_3 z)...

A code C in a generalised quadrangle $${\mathcal {Q}}$$ is defined to be subset of the vertex set point-line incidence graph $${\Gamma }$$ . The minimum distance $$\delta $$ smallest between pair distinct elements C. metric gives rise partition $$\{C,C_1,\ldots ,C_\rho \}$$ , where $$\rho maximum any and its nearest element Since diameter 4, both are at most 4. If =4$$ then partial ovoid or spr...

In this paper, we investigate the quantity $m_q:=\min_{\chi\ne \chi_0} | L^\prime/L(1,\chi)|$, as $q\to \infty$ over primes, where $L(s,\chi)$ is Dirichlet $L$-function attached to a non trivial character modulo $q$. Our main result shows that $m_q \ll \log\log q/\sqrt{\log q}$. We also compute $m_q$ for every odd prime $q$ up $10^7$. As consequence numerically verified $q$, $3 \le q 10^7$, hav...

Изучены $SU$-линейные операции в комплексных кобордизмах и доказано, что все они порождаются известными геометрическими операциями $\partial_i$. Для теории $c_1$-сферических бордизмов $W$ описаны умножения на проекторы $MU \to W$. Кроме того, исследованы комплексные ориентации соответствующие им формальные группы $F_W$. Связь между формальными группами $F_W$ кольцом коэффициентов $W_*$ изучалас...

The average distance of a vertex $v$ of a connected graph $G$is the arithmetic mean of the distances from $v$ to allother vertices of $G$. The proximity $pi(G)$ and the remoteness $rho(G)$of $G$ are defined as the minimum and maximum averagedistance of the vertices of $G$. In this paper we investigate the difference between proximity or remoteness and the classical distanceparameters diameter a...

The transformation theory of the Appell $F_2(a,b_1,b_2;c_1,c_2;x,y)$ double hypergeometric function is used to obtain a set series representations $F_2$ which provide an efficient way evaluate for real values its arguments $x$ and $y$ generic complex parameters $a,b_1, b_2, c_1$ $c_2$ (i.e. in nonlogarithmic case). This study rests on classical approach where usual representation other that app...