A CaAl 2 Si 2 -Type Magnetic Semiconductor (Sr, Na)(Zn, Mn)2Sb2 Isostructural to 122-Type Iron-Based Superconductors

A new diluted magnetic semiconductor (Sr, Na)(Zn, Mn)2Sb2 has been successfully synthesized by doping Na and Mn into the parent compound SrZn 2 Sb 2 , which has a CaAl 2 Si 2 -type crystal structure (space group P 3 ¯ m 1 , No. 164, h P 5 ) isostructural to the 122-type iron-based superconductor CaFe 2 As 2 . No magnetic ordering has been observed when only spins are doped by (Zn, Mn) substitution. Only with carriers codoped by (Sr, Na) substitution, a ferromagnetic ordering occurs below the maximum Curie temperature T C ∼9.5 K. Comparing with other CaAl 2 Si 2 -type diluted magnetic semiconductors, we will show that negative chemical pressure suppresses the Curie temperature.

A Multiple Fixed Point Result for θ , ϕ , ψ -Type Contractions in the Partially Ordered s -Distance Spaces with an Application

In this manuscript, the aim is to prove a multiple fixed point (FP) result for partially ordered s -distance spaces under θ , ϕ , ψ -type weak contractive condition. The result will generalize some well-known results in literature such as coupled FP (Guo and Lakshmikantham, 1987), triple fixed point (Berinde and Borcut, 2011), and quadruple FP results (Karapinar, 2011). Moreover, to validate the result, an application for the existence of solution of a system of integral equations is also provided.

Cyclic Mappings and Further Results in B-Metric-Like Spaces

Fixed point problem of many mappings has been widely studied in the research work of fixed point theory. The generalized metric space is one of the research objects of fixed point theory. B-metric-like space is one of the generalized metric spaces; in fact, the research work in B-metric-like spaces is attractive. The intention of this paper is to introduce the concept of other cyclic mappings, named as L β -type cyclic mappings in the setting of B-metric-like space, study the existence and uniqueness of fixed point problem of L β -type cyclic mapping, and obtain some new results in B-metric-like spaces. Furthermore, the main results in this paper are illustrated by a concrete example. The work of this paper extend and promote the previous results in B-metric-like spaces.

Equivariant multiplicities of simply-laced type flag minors

Let g \mathfrak {g} be a finite simply-laced type simple Lie algebra. Baumann-Kamnitzer-Knutson recently defined an algebra morphism D ¯ \overline {D} on the coordinate ring C [ N ] \mathbb {C}[N] related to Brion’s equivariant multiplicities via the geometric Satake correspondence. This map is known to take distinguished values on the elements of the MV basis corresponding to smooth MV cycles, as well as on the elements of the dual canonical basis corresponding to Kleshchev-Ram’s strongly homogeneous modules over quiver Hecke algebras. In this paper we show that when g \mathfrak {g} is of type A n A_n or D 4 D_4 , the map D ¯ \overline {D} takes similar distinguished values on the set of all flag minors of C [ N ] \mathbb {C}[N] , raising the question of the smoothness of the corresponding MV cycles. We also exhibit certain relations between the values of D ¯ \overline {D} on flag minors belonging to the same standard seed, and we show that in any A D E ADE type these relations are preserved under cluster mutations from one standard seed to another. The proofs of these results partly rely on Kang-Kashiwara-Kim-Oh’s monoidal categorification of the cluster structure of C [ N ] \mathbb {C}[N] via representations of quiver Hecke algebras.

On Some New Simpson’s Formula Type Inequalities for Convex Functions in Post-Quantum Calculus

In this work, we prove a new (p,q)-integral identity involving a (p,q)-derivative and (p,q)-integral. The newly established identity is then used to show some new Simpson’s formula type inequalities for (p,q)-differentiable convex functions. Finally, the newly discovered results are shown to be refinements of comparable results in the literature. Analytic inequalities of this type, as well as the techniques used to solve them, have applications in a variety of fields where symmetry is important.

Variational characterizations of weighted Hardy spaces and weighted spaces

This paper obtains new characterizations of weighted Hardy spaces and certain weighted $BMO$ type spaces via the boundedness of variation operators associated with approximate identities and their commutators, respectively.

Some New Simpson’s-Formula-Type Inequalities for Twice-Differentiable Convex Functions via Generalized Fractional Operators

From the past to the present, various works have been dedicated to Simpson’s inequality for differentiable convex functions. Simpson-type inequalities for twice-differentiable functions have been the subject of some research. In this paper, we establish a new generalized fractional integral identity involving twice-differentiable functions, then we use this result to prove some new Simpson’s-formula-type inequalities for twice-differentiable convex functions. Furthermore, we examine a few special cases of newly established inequalities and obtain several new and old Simpson’s-formula-type inequalities. These types of analytic inequalities, as well as the methodologies for solving them, have applications in a wide range of fields where symmetry is crucial.

Optimal L p – L q -Type Decay Rates of Solutions to the Three-Dimensional Nonisentropic Compressible Euler Equations with Relaxation

In this paper, we consider the three-dimensional Cauchy problem of the nonisentropic compressible Euler equations with relaxation. Following the method of Wu et al. (2021, Adv. Math. Phys. Art. ID 5512285, pp. 1–13), we show the existence and uniqueness of the global small H k k ⩾ 3 solution only under the condition of smallness of the H 3 norm of the initial data. Moreover, we use a pure energy method with a time-weighted argument to prove the optimal L p – L q 1 ⩽ p ⩽ 2 , 2 ⩽ q ⩽ ∞ -type decay rates of the solution and its higher-order derivatives.

Twistor constructions for higher-spin extensions of (self-dual) Yang-Mills

We present the inverse Penrose transform (the map from spacetime to twistor space) for self-dual Yang-Mills (SDYM) and its higher-spin extensions on a flat background. The twistor action for the higher-spin extension of SDYM (HS-SDYM) is of $$ \mathcal{BF} $$ BF -type. By considering a deformation away from the self-dual sector of HS-SDYM, we discover a new action that describes a higher-spin extension of Yang-Mills theory (HS-YM). The twistor action for HS-YM is a straightforward generalization of the Yang-Mills one.

The wandering subspace property and Shimorin’s condition of shift operator on the weighted Bergman spaces

In the present paper, we first study the wandering subspace property of the shift operator on the $$I_{a}$$ I a type zero based invariant subspaces of the weighted Bergman spaces $$L_{a}^{2}(dA_{n})(n=0,2)$$ L a 2 ( d A n ) ( n = 0 , 2 ) via the spectrum of some Toeplitz operators on the Hardy space $$H^{2}$$ H 2 . Second, we give examples to show that Shimorin’s condition for the shift operator fails on the $$I_{a}$$ I a type zero based invariant subspaces of the weighted Bergman spaces $$L_{a}^{2}(dA_{\alpha })(\alpha >0)$$ L a 2 ( d A α ) ( α > 0 ) .