subject to Gj(x, t) ≤ 0 for all t ∈ Tj , j ∈ q, Hk(x, s) = 0 for all s ∈ Sk, k ∈ r, x ∈ X, where q and r are positive integers, X is a nonempty open convex subset of Rn (n-dimensional Euclidean space), for each j ∈ q ≡ {1, 2, . . . , q} and k ∈ r, Tj and Sk are compact subsets of complete metric spaces, f and g are real-valued functions defined on X, for each j ∈ q, z → Gj(z, t) is a real-value...

We derive the full set of field equations for metric-affine version Myrzakulov gravity model and also extend this family theories to a broader one. More specifically, we consider whose gravitational Lagrangian is given by F(R,T,Q,T,D) where T, Q are torsion non-metricity scalars, T trace energy-momentum tensor D divergence dilation current. then linear case aforementioned theory and, assuming c...

For all 0 < t ≤ 1, we define a locally Euclidean metric ρt on R . These metrics are invariant under Euclidean isometries and, if t increases to 1, converge to the Euclidean metric dE . This research is motivated by expanding universe. key words. locally Euclidean metric PACS number(s). 98.80.Jk Mathematics Subject Classifications (2000). 85A40, 57M50 1 The metric ρt Let dE denote the Euclidean ...

We prove the existence of equivariant finite time blow-up solutions for the wave map problem from R2+1 → S2 of the form u(t, r) = Q(λ(t)r)+R(t, r) where u is the polar angle on the sphere, Q(r) = 2 arctan r is the ground state harmonic map, λ(t) = t−1−ν , and R(t, r) is a radiative error with local energy going to zero as t→ 0. The number ν > 1 2 can be described arbitrarily. This is accomplish...

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Let $SM_n(\mathbb{R})^g$ denote $g$-tuples of $n \times n$ real symmetric matrices and set $SM(\mathbb{R})^g = \cup_n SM_n(\mathbb{R})^g$. A free quadrilateral is the collection tuples $X \in SM(\mathbb{R})^2$ which have positive semidefinite evaluation on linear equations defining a classical quadrilateral. Such closed under rich class convex combinations called matrix combination. That is, gi...

The dually conjugate Hopf algebras Funp,q(R) and Up,q(R) associated with the two-parametric (p, q)-Alexander-Conway solution (R) of the Yang-Baxter equation are studied. Using the Hopf duality construction, the full Hopf structure of the quasitriangular enveloping algebra Up,q(R) is extracted. The universal T matrix for Funp,q(R) is derived. While expressing an arbitrary group element of the qu...

In the framework of McKay correspondence we determine, for every finite subgroup Γ of SL4C, how the finite dimensional irreducible representations of SL4C decompose under the action of Γ. Let h be a Cartan subalgebra of sl4C and let ̟1, ̟2, ̟3 be the corresponding fundamental weights. For (p, q, r) ∈ N, the restriction πp,q,r|Γ of the irreducible representation πp,q,r of highest weight p̟1 + q̟2 + r̟...