We study the global dimension function $${\text {gldim}}:{\text {Aut}}\backslash {\text {Stab}}{\mathcal {D}}/\mathbb {C}\rightarrow \mathbb {R}_{\ge 0}$$ on quotient of space Bridgeland stability conditions a triangulated category $${\mathcal {D}}$$ as well Toda’s Gepner equation $$\Phi (\sigma )=s\cdot \sigma $$ for some $$\sigma \in and $$(\Phi ,s)\in {Aut}}{\mathcal {D}}\times {C}$$ . For b...

Let E be a real Banach space and let A : E → E be a Lipschitzian generalized strongly accretive operator. Let z ∈ E and x0 be an arbitrary initial value in E for which the steepest descent approximation scheme is defined by xn+1 = xn − αn(Ayn − z), yn = xn − βn(Axn − z), n = 0, 1, 2 . . . , where the sequences {αn} and {βn} satisfy the following conditions: (i) 0 ≤ αn, βn ≤ 1, (ii) ∞

We identify Melrose’s suspended algebra of pseudodifferential operators with a subalgebra of the algebra of parametric pseudodifferential operators with parameter space R. For a general algebra of parametric pseudodifferential operators, where the parameter space may now be a cone Γ ⊂ Rp, we construct a unique “symbol valued trace”, which extends the L2–trace on operators of small order. This a...

We identify Melrose’s suspended algebra of pseudodifferential operators with a subalgebra of the algebra of parametric pseudodifferential operators with parameter space R. For a general algebra of parametric pseudodifferential operators, where the parameter space may now be a cone Γ ⊂ Rp, we construct a unique “symbol valued trace”, which extends the L2–trace on operators of small order. This c...

In this paper we study *-Conformal {\eta}-Ricci soliton on Sasakian manifolds. Here, discuss some curvature properties manifold admitting soliton. We obtain significant results in manifolds satisfying R({\xi},X).S = 0, S({\xi},X).R {\overline}P({\xi},X).S where {\overline}P is Pseudo-projective tensor.The conditions for {\Phi}-conharmonically flat and {\Phi}-projectively have been obtained arti...

The following convective Brinkman-Forchheimer (CBF) equations (or damped Navier-Stokes equations) with potential$ \begin{equation*} \frac{\partial \boldsymbol{y}}{\partial t}-\mu \Delta\boldsymbol{y}+(\boldsymbol{y}\cdot\nabla)\boldsymbol{y}+\alpha\boldsymbol{y}+\beta|\boldsymbol{y}|^{r-1}\boldsymbol{y}+\nabla p+\Psi(\boldsymbol{y})\ni\boldsymbol{g},\ \nabla\cdot\boldsymbol{y} = 0, \end{equatio...

Our first aim is to clarify the results obtained by Lidskii devoted decomposition on root vector system of non-selfadjoint operator. We use a technique entire function theory and introduce so-called Schatten–von Neumann class convergence exponent. Considering strictly accretive operators satisfying special conditions formulated in terms norm, we construct sequence contours power type that contr...

Given a dissipative operator \(A\) on complex Hilbert space \(\mathcal{H}\) such that the quadratic form \(f \mapsto \text{Im}\langle f, Af \rangle\) is closable, we give necessary and sufficient condition for an extension of to still be dissipative. As applications, describe all maximally accretive extensions strictly positive symmetric operators highly singular first-order interval.