Based on conservation laws for surface layer integrals critical points of causal variational principles, it is shown how jet spaces can be endowed with an almost-complex structure. We analyze under which conditions the structure integrated to a canonical complex Combined scalar product expressed by integral, we obtain Hilbert space $\mathfrak{h}$. The Euler-Lagrange equations principle describe...

Let $\mathbb F$ be a finite field. Consider direct sum $V$ of an infinite number copies F$, consider the dual space $V^\diamond$, i.~e., product F$. ${\mathbb V}=V\oplus V^\diamond$. The object paper is group $\mathbf{GL}$ continuous linear operators in V$. We reduce theory unitary representations to projective certain category whose morphisms are relations finite-dimensional spaces over In fac...

For $A,Bin M_{nm},$ we say that $A$ is left matrix majorized (resp. left matrix submajorized) by $B$ and write $Aprec_{ell}B$ (resp. $Aprec_{ell s}B$), if $A=RB$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $R.$ Moreover, we define the relation $sim_{ell s} $ on $M_{nm}$ as follows: $Asim_{ell s} B$ if $Aprec_{ell s} Bprec_{ell s} A.$ This paper characterizes all linear p...

the overall aim of this paper is to highlight a transcendental usage of the religion of islamin the qur’an. i will show that the notion of islamas a unitary religion is used in the qur’an as a genus for religions (adyan) which have appeared throughout human history. this usage will show that there is a sense of religion which guarantees the essential unity of all religions and prepares us to un...

New insight into the correspondence between Quantum Chaos and Random Matrix Theory is gained by developing a semiclassical theory for the autocor-relation function of spectral determinants. We study in particular the unitary operators which are the quantum versions of area preserving maps. The relevant Random Matrix ensembles are the Circular ensembles. The resulting semiclassical expressions d...

Hughston has recently proposed a stochastic extension of the Schrödinger equation, expressed as a stochastic differential equation on projective Hilbert space. We derive new projective Hilbert space identities, which we use to give a general proof that Hughston’s equation leads to state vector collapse to energy eigenstates, with collapse probabilities given by the quantum mechanical probabilit...