Methyl methacrylate particles with amino groups on the surface: Colloid stability and sorption of biologically active substances

The present article investigates the influence of dispersion medium on the aggregate stability of cross-linked poly-(methyl methacrylate) particles on the surface layer of which aliphatic amino groups are localized. It is shown that particle size depends on the ionic strength of dispersion medium. The research determines the optimal content of cross-linked agent, ethylene glycol dimetharylate that results in the formation of cationic particles being stable in saline. Particle modification is performed by bovine serum albumin and luminophore fluorescein 5(6)-isothiocyanate. Protein sorption is observed not to influence luminescent properties of the particles. It is also determined that due to the aggregate stability of particles obtained from 5?wt% of ethylene glycol dimethacrylate in saline, the monodispersity and the absence of inversion of zeta potential in wide pH range is retained, such particles may be considered as perspective carriers of biologically active substances.     

Acid‐Cleavable Unimolecular Micelles from Amphiphilic Star Copolymers for Triggered Release of Anticancer Drugs

In this contribution, amphiphilic star copolymers (H40‐star‐PCL‐a‐PEG) with an H40 hyperbranched polyester core and poly(ε‐caprolactone)‐a‐poly(ethylene glycol) copolymer arms linked with acetal groups are synthesized using ring‐opening polymerization and a copper (I)‐catalyzed alkyne‐azide cycloaddition click reaction. The acid‐cleavable acetal groups between the hydrophilic and hydrophobic segments of the arms endow the amphiphilic star copolymers with pH responsiveness. In aqueous solution, unimolecular micelles can be formed with good stability and a unique acid degradability, as is desirable for anticancer drug carriers. For the model drug of doxorubicin, the in vitro release behavior, intracellular release, and inhibition of proliferation of HeLa cells show that the acid‐cleavable unimolecular micelles with anticancer activity can be dissociated in an acidic environment and efficiently internalized by HeLa cells. Due to the acid‐cleavable and biodegradable nature, unimolecular micelles from amphiphilic star copolymers are promising for applications in intracellular drug delivery for cancer chemotherapy.

     

A tensor product of the Steinberg module and a certain simple kG(pr)-module

Let G be a connected, semisimple, and simply connected algebraic group defined and split over the finite field of order p, and let G(q) be the corresponding finite Chevalley or twisted group, where q = p^r. Recently, Anwar determines the direct sum decomposition of the tensor product of the rth Steinberg module and a simple G-module with a (p,r)-minuscule highest weight λ. In this paper, we determine that of the tensor product regarded as a module for G(q) under some weak assumptions for λ.     

Odd length for even hyperoctahedral groups and signed generating functions

We define a new statistic on the even hyperoctahedral groups which is a natural analogue of the odd length statistic recently defined and studied on Coxeter groups of types $A$ and $B$. We compute the signed (by length) generating function of this statistic over the whole group and over its maximal and some other quotients and show that it always factors nicely. We also present some conjectures.     

On Lorentzian Ricci solitons on nilpotent Lie groups

The aim of this article is to exhibit the variety of different Ricci soliton structures that a nilpotent Lie group can support when one allows for the metric tensor to be Lorentzian. In stark contrast to the Riemannian case, we show that a nilpotent Lie group can support a number of non‐isometric Lorentzian Ricci soliton structures with decidedly different qualitative behaviors and that Lorentzian Ricci solitons need not be algebraic Ricci solitons. The analysis is carried out by classifying all left invariant Lorentzian metrics on the connected, simply‐connected five‐dimensional Lie group having a Lie algebra with basis vectors and and non‐trivial bracket relations and , investigating the various curvature properties of the resulting families of metrics, and classifying all Lorentzian Ricci soliton structures.     

On separating a fixed point from zero by invariants

Assume a fixed point v∈V^G can be separated from zero by a homogeneous invariant f∈𝕜[V]^G of degree p^rd, where p>0 is the characteristic of the ground field 𝕜 and p,d are coprime. We show that then v can also be separated from zero by an invariant of degree p^r, which we obtain explicitly from f. It follows that the minimal degree of a homogeneous invariant separating v from zero is a p-power.     

Structures of the twisted N = 1 Schrödinger–Neveu–Schwarz algebra

In this paper, we determine the universal central extension, derivation algebra and automorphism group of the twisted N = 1 Schrödinger–Neveu–Schwarz algebra. Furthermore, we generalize these results to the generalized twisted N = 1 Schrödinger–Neveu–Schwarz algebra in the final section.     

Free groups in a normal subgroup of the field of fractions of a skew polynomial ring

Let k(t) be the field of rational functions over the field k, let σ be a k-automorphism of K = k(t), let D = K(X;σ) be the ring of fractions of the skew polynomial ring K[X;σ], and let D^? be the multiplicative group of D. We show that if N is a noncentral normal subgroup of D^?, then N contains a free subgroup. We also prove that when k is algebraically closed and σ has infinite order, there exists a specialization from D to a quaternion algebra. This allows us to explicitly present free subgroups in D^?.     

Central Schur rings over the projective special linear groups

In [1 Bannai, E. (1991). Subschemes of some association schemes. J. Algebra 14:167–188.[Crossref], [Web of Science ®] , [Google Scholar]], Bannai presents a fusion condition and uses this to consider central Schur rings (S-rings) over the simple groups PSL(2,q) where q is a prime power. In this paper, we concretely describe all such S-rings in terms of symmetric S-rings over cyclic groups. The final section discusses counting these.     

Nearly m-embedded subgroups and solvability of finite groups

A subgroup A of a finite group G is called {1≤G}-embedded in G if for each two subgroups K≤H of G, where K is a maximal subgroup of H, A either covers the pair (K,H) or avoids it. Moreover, a subgroup H of G is called nearly m-embedded in G if G has a subgroup T and a {1≤G}-embedded subgroup C such that G?=?HT and H∩T≤C≤H. In this paper, we mainly prove that G is solvable if and only if its Sylow 3-subgroups, Sylow 5-subgroups and Sylow 7-subgroups are nearly m-embedded in G.