In this paper, we investigate properties concerning some recently introduced finite coarse shape invariants—the k-th group of a pointed topological space and the relative pair. We define notion sequence pair X,X0,x0 as an analogue homotopy (coarse) sequences show that for any pair, corresponding is chain. On other hand, construct example metric continua whose fails to be exact. Finally, using a...

In this paper we present COMET, a Gaussian process emulator of the galaxy power spectrum multipoles in redshift-space. The model predictions are based on one-loop perturbation theory and consider two alternative descriptions redshift-space distortions: one that performs full expansion real- to mapping, as recent effective field models, another preserves non-perturbative impact small-scale veloc...

2. For any point x0 ∈ R+ and any subgradient a ∈ ∂g(x0) all coordinates of a are nonpositive. If in addition g(x0) > y0 then all coordinates of a are negative. 3. For any point x0 ∈ R+ such that g(x0) > y0 we have: h ◦ g(x0) ≤ Cd! ddV (x0) , where V (x) ≡ ∏d k=1 xk for x ∈ R+. 4. The function h reverses partial order on Rd+: if x1 < x2 then g(x1) ≥ g(x2) and the last inequality is strict if g(x...

Figure 1. Finite state machine for a Markov chain X0 → X1 → X2 → · · · → Xn where the random variables Xi’s take values from I = {S1, S2, S3}. The numbers T (i, j)’s on the arrows are the transition probabilities such that Tij = P (Xt+1 = Sj|Xt = Si). Definition 1.2. We say that (Xn)n≥0 is a Markov chain with initial distribution λ and transition matrix T if (i) X0 has distribution λ; (ii) for ...

This study is about the effects of Yukawa-like corrections to Newtonian potential on existence and stability noncollinear equilibrium points in a circular restricted three-body problem when bigger primary an oblate spheroid. It observed that ∂x0/∂λ = 0 ∂y0/∂λ at λ0 1/2, so we have critical point 1/2 which maximum minimum values x0 y0 can be obtained, where λ ∈ (0, ∞) range Yukawa force (x0, y0)...

A strong maximal principle for the operator (a/st) + L, is a statement of the form: "for each open 1 c [0, oo) x Rd and each (to, x0) e 9 there is a set Y(to, x0) 91 with the property that (af/lt) + LJf _ 0 on !(to, x0) and f(to, x0) = supg(toXO)f(t, x) imply f _ f(to, xO) on 9(to, x0)." Of course, in order for a strong maximum principle to be very interesting it must describe the set 9(to, x0)...

The Jacobian J0(23) of the modular curve X0(23) is a semi-stable abelian variety over Q with good reduction outside 23. It is simple. We prove that every simple semi-stable abelian variety over Q with good reduction outside 23 is isogenous over Q to J0(23). 2010 Mathematics Subject Classification. Primary 14L15; Secondary 11G18, 11R37.

We study stochastic differential equations (SDEs) with multiplicative Stratonovich-type noise of the formdXt=b(Xt)dt+σ(Xt)∘dWt,X0=x0∈Rd,t⩾0, a possibly singular drift b∈Lp(Rd), p>d and p⩾2, show that such SDEs can be approximated by random ordinary smoothing at same time. further prove support theorem for this class in rather simple way using Girsanov theorem.