Published volumes
19521968 Revista de la Unión Matemática Argentina y de la Asociación Física Argentina
19441951 Revista de la Unión Matemática Argentina; órgano de la Asociación Física Argentina
19361944

Volume 60, number 1 (2019)
June 2019
Primary decomposition and secondary representation of modules.
Masoumeh Hasanzad, Jafar A'zami
In this paper we study the notions of primary decomposition and
secondary representation of modules over a commutative ring with
identity. Also we review these concepts over injective and projective
modules.

1–8 
Lie $n$multiplicative mappings on triangular $n$matrix rings.
Bruno L. M. Ferreira, Henrique Guzzo Jr.
We extend to triangular $n$matrix rings and Lie $n$multiplicative maps a
result about Lie multiplicative maps on triangular algebras due to Xiaofei Qi
and Jinchuan Hou.

9–20 
Higher order mean curvatures of SAC halflightlike submanifolds of indefinite almost contact manifolds.
Fortuné Massamba, Samuel Ssekajja
We introduce higher order mean curvatures of screen almost conformal (SAC)
halflightlike submanifolds of indefinite almost contact manifolds, admitting a
semisymmetric nonmetric connection. We use them to generalize some known
results by Duggal and Sahin on totally umbilical halflightlike submanifolds
[Int. J. Math. Math. Sci. 2004, no. 68, 37373753].
Also, we derive a new integration formula via the divergence of some special
vector fields tangent to these submanifolds, which we later use to characterize
minimal and maximal submanifolds. Several examples, where possible, are also
included to illustrate the main concepts.

21–44 
Branching laws: some results and new examples.
Oscar Márquez, Sebastián Simondi, Jorge A. Vargas
For a connected, noncompact simple matrix Lie group $G$ so that a maximal
compact subgroup $K$ has a three dimensional simple ideal, in this note we
analyze the admissibility of the restriction of irreducible square integrable
representations for the ambient group when they are restricted to certain
subgroups that contain the three dimensional ideal. In this setting we provide
a formula for the multiplicity of the irreducible factors. Also, for general
$G$ such that $G/K$ is an Hermitian $G$manifold we give a necessary and
sufficient condition so that an arbitrary square integrable representation of
the ambient group is admissible over the semisimple factor of $K$.

45–59 
On the structure of split involutive HomLie color algebras.
Valiollah Khalili
In this paper we study the structure of arbitrary split involutive regular
HomLie color algebras. By developing techniques of connections of roots for
this kind of algebras, we show that such a split involutive regular HomLie
color algebra $\mathcal{L}$ is of the form
$\mathcal{L}=\mathcal{U}\oplus\sum_{[\alpha]\in\Pi/\sim} I_{[\alpha]}$, with
$\mathcal{U}$ a subspace of the involutive abelian subalgebra $\mathcal{H}$ and
any $I_{[\alpha]}$, a welldescribed involutive ideal of $\mathcal{L}$, satisfying
$[I_{[\alpha]}, I_{[\beta]}]=0$ if $[\alpha]\neq[\beta]$. Under certain conditions, in the
case of $\mathcal{L}$ being of maximal length, the simplicity of the algebra is
characterized and it is shown that $\mathcal{L}$ is the direct sum of the
family of its minimal involutive ideals, each one being a simple split
involutive regular HomLie color algebra. Finally, an example will be provided
to characterise the inner structure of split involutive HomLie color algebras.

61–77 
The multivariate bisection algorithm.
Manuel López Galván
The aim of this paper is to study the bisection method in $\mathbb{R}^n$.
We propose a multivariate bisection method supported by the
Poincaré–Miranda theorem in order to solve nonlinear systems of equations.
Given an initial cube satisfying the hypothesis of the Poincaré–Miranda theorem,
the algorithm performs congruent refinements through its center by
generating a root approximation. Through preconditioning we will prove the
local convergence of this new root finder methodology and moreover we will
perform a numerical implementation for the two dimensional case.

79–98 
Some new $Z$eigenvalue localization sets for tensors and their applications.
Zhengge Huang, Ligong Wang, Zhong Xu , Jingjing Cui
In this paper some new $Z$eigenvalue localization sets for general tensors are
established, which are proved to be tighter than those newly derived by Wang et
al. [Discrete Contin. Dyn. Syst. Ser. B, 22 (2017), 187–198].
Also, some relationships between the $Z$eigenvalue inclusion sets presented by
Wang et al. and the new $Z$eigenvalue localization sets for tensors are given.
Besides, we discuss the effects of orthonormal transformations for the proposed
sets. As applications of the proposed sets, some improved upper bounds for the
$Z$spectral radius of weakly symmetric nonnegative tensors are given. Numerical
examples are also given to verify the advantages of our proposed results over
some known ones.

99–119 
Direct theorems of trigonometric approximation for variable exponent Lebesgue spaces.
Ramazan Akgün
Jackson type direct theorems are considered in variable exponent Lebesgue
spaces $L^{p(x)}$ with exponent $p(x)$ satisfying $1\leq
\operatorname{ess\,inf}_{x\in [0,2\pi ]}p(x)$, $\operatorname{ess\,sup}_{x\in
[0,2\pi]}p(x) < \infty$, and the Dini–Lipschitz condition. Jackson
type direct inequalities of trigonometric approximation are obtained for the
modulus of smoothness based on one sided Steklov averages
\[
\mathfrak{Z}_{v}f(\cdot) := \frac{1}{v}\int\nolimits_{0}^{v}f
(\cdot+t) \,dt
\]
in these spaces. We give the main properties of the modulus of smoothness
\[
\Omega_{r}(f,v)_{p(\cdot)} := \left\Vert
(\mathbf{I}\mathfrak{Z}_{v})^{r}f\right\Vert_{p(\cdot)}\quad
(r\in \mathbb{N})
\]
in $L^{p(x)}$, where $\mathbf{I}$ is the identity operator. An
equivalence of the modulus of smoothness and Peetre's $K$functional is
established.

121–135 
Pricing American put options under stochastic volatility using the Malliavin derivative.
Mohamed Kharrat
The aim of this paper is to develop a methodology based on Malliavin
calculus, in order to price American options under stochastic volatility. This
leads to compute the conditional expectation $\mathbb{E}(P_{t}(X_{t},
V_{t})\mid(X_{l},V_{l}))$ for any $ 0\leq l < t$, where $V_{t}$ is generated by the
CoxIngersollRoss (CIR) process. Some simulations and comparisons are
given.

137–147 
Trajectorial market models: arbitrage and pricing intervals.
Sebastián E. Ferrando, Alfredo L. González, Iván L. Degano, Massoomeh Rahsepar
The paper develops general, nonprobabilistic market models based on trajectory
sets and minmax price bounds leading to price intervals for European options.
The approach provides the trajectory based analogue of a martingale process as
well as a generalization that allows a limited notion of arbitrage in the
market while still providing coherent option prices. An illustrative example is
described in detail. Several properties of the price bounds are obtained, in
particular a connection with risk neutral pricing is established for trajectory
markets associated to a continuoustime martingale model.

149–185 
Relative modular uniform approximation by means of the power series method with applications.
Kuldip Raj, Anu Choudhary
We introduce the notion of relative convergence by means of a four dimensional
matrix in the sense of the power series method, which includes Abel's as well as
Borel's methods, to prove a Korovkin type approximation theorem by using the
test functions $\{1,y,z,y^{2}+z^{2}\}$ and a double sequence of positive linear
operators defined on modular spaces. We also endeavor to examine some
applications related to this new type of approximation.

187–208 
Top local cohomology modules over local rings and the weak goingup property.
Asghar Farokhi, Alireza Nazari
Let $(R,\mathfrak{m})$ be a Noetherian local ring and let $\widehat{R}$ denote the
$\mathfrak{m}$adic completion of $R$. In this paper, we introduce the concept of the
weak goingup property for the extension $R\subseteq \widehat{R}$ and we give
some characterizations of this property. In particular, we show that this
property is equivalent to the strong form of the Lichtenbaum–Hartshorne
Vanishing Theorem. Also, when $R$ satisfies the weak goingup property, we show
that for a finitely generated $R$module $M$ of dimension $d$, and ideals $\mathfrak{a}$
and $\mathfrak{b}$ of $R$, we have $\operatorname{Att}_{R}(\operatorname{H}^{d}_{\mathfrak{a}}(M)) =
\operatorname{Att}_{R}(\operatorname{H}^{d}_{\mathfrak{b}}(M))$ if and only if $\operatorname{H}^{d}_{\mathfrak{a}}(M)\cong
\operatorname{H}^{d}_{\mathfrak{b}}(M)$, and we find a criterion for the cofiniteness of Artinian top
local cohomology modules.

209–215 
Formal torsors under reductive group schemes.
Benedictus Margaux
We consider the algebraization problem for torsors over a proper formal scheme
under a reductive group scheme. Our results apply to the case of semisimple
group schemes (which is addressed in detail).

217–224 
Hörmander conditions for vectorvalued kernels of singular integrals and their commutators.
Andrea L. Gallo, Gonzalo H. Ibañez Firnkorn, María Silvina Riveros
We study Coifman type estimates and weighted norm inequalities for singular
integral operators and their commutators, given by the convolution with a
vectorvalued kernel. We define a weaker Hörmander type condition
associated with Young functions for the vectorvalued kernels. With this
general framework we obtain as an example the result for the square operator
and its commutator given in [M. Lorente, M. S. Riveros, and A. de la Torre,
J. Math. Anal. Appl. 336 (2007), no. 1, 577–592].

225–245 
On the selfconjugateness of differential forms on bounded domains.
Ricardo Abreu Blaya, Juan Bory Reyes, Efrén Morales Amaya, José María Sigarreta Almira
Suppose $\Omega$ is a bounded domain in $\mathbb{R}^n$ with boundary $\Gamma$ and let
$\mathcal{W}$ be a nonhomogeneous differential form harmonic in $\Omega$ and
Höldercontinuous in $\Omega\cup\Gamma$. In this paper we study and obtain
some necessary and sufficient conditions for the selfconjugateness of $\mathcal{W}$ in
terms of its boundary value $\mathcal{W}_\Gamma=\omega$.

247–256 
A remark on transSasakian 3manifolds.
Yaning Wang, Wenjie Wang
Let $M$ be a transSasakian $3$manifold of type $(\alpha,\beta)$. In this
paper, we give a negative answer to the question proposed by S. Deshmukh
[Mediterr. J. Math. 13 (2016), no. 5, 2951–2958], namely we prove
that the differential equation $\nabla\beta=\xi(\beta)\xi$ on $M$ does not
necessarily imply that $M$ is homothetic to either a Sasakian or cosymplectic
manifold even when $M$ is compact. Many examples are constructed to illustrate
this result.

257–264 
Finite
dimensional Hopf algebras over the KacPaljutkin algebra $H_8$.
Yuxing Shi
Let $H_8$ be the Kac–Paljutkin algebra [Trudy Moskov. Mat.
Obšč. 15 (1966), 224–261], which is the neither
commutative nor cocommutative semisimple eight dimensional Hopf
algebra. All simple Yetter–Drinfel'd modules over $H_8$ are given,
and finitedimensional Nichols algebras over $H_8$ are determined
completely. It turns out that they are all of diagonal type. In
fact, they are of Cartan types $A_1$, $A_2$, $A_2\times A_2$,
$A_1\times \cdots \times A_1$, and $A_1\times \cdots \times
A_1\times A_2$, respectively. By the way, we calculate
Gelfand–Kirillov dimensions for some Nichols algebras. As an
application, we complete the classification of the
finitedimensional Hopf algebras over $H_8$ according to the
lifting method.

265–298 
Volume 60, number 2 (2019)
December 2019
Linear Poisson structures and HomLie algebroids.
Esmaeil Peyghan, Amir Baghban, and Esa Sharahi
Considering HomLie algebroids in some special cases, we obtain some results of
Lie algebroids for HomLie algebroids. In particular, we introduce the local
splitting theorem for HomLie algebroids. Moreover, linear HomPoisson
structure on the dual Hombundle will be introduced and a onetoone
correspondence between HomPoisson structures and HomLie algebroids will be
presented. Also, we introduce Hamiltonian vector fields by using linear Poisson
structures and show that there exists a relation between these vector fields
and the anchor map of a HomLie algebroid.

299–313 
On supersolvable
groups whose maximal subgroups of the Sylow subgroups are
subnormal.
Pengfei Guo, Xingqiang Xiu, and Guangjun Xu
A finite group $G$ is called an MSN$^{*}$group if it is supersolvable, and all
maximal subgroups of the Sylow subgroups of $G$ are subnormal in $G$. A group
$G$ is called a minimal nonMSN$^{*}$group if every proper subgroup of $G$ is
an MSN$^{*}$group but $G$ itself is not. In this paper, we obtain a complete
classification of minimal nonMSN$^{*}$groups.

315–322 
Periodic
solutions of Euler–Lagrange equations in an anisotropic
Orlicz–Sobolev space setting.
Fernando D. Mazzone and Sonia Acinas
We consider the problem of finding periodic solutions of certain
Euler–Lagrange equations which include, among others, equations involving the
$p$Laplace operator and, more generally, the $(p,q)$Laplace operator. We
employ the direct method of the calculus of variations in the framework of
anisotropic Orlicz–Sobolev spaces. These spaces appear to be useful in
formulating a unified theory of existence of solutions for such a problem.

323–341 
Classification of
left invariant Hermitian structures on 4dimensional noncompact rank one
symmetric spaces.
Srdjan Vukmirović, Marijana Babić, and Andrijana Dekić
The only 4dimensional noncompact rank one symmetric spaces are
$\mathbb{C}H^2$ and $\mathbb{R}H^4$. By the classical results of Heintze, one
can model these spaces by real solvable Lie groups with left invariant metrics.
In this paper we classify all possible left invariant Hermitian structures on
these Lie groups, i.e., left invariant Riemannian metrics and the corresponding
Hermitian complex structures. We show that each metric from the classification
on $\mathbb{C}H^2$ admits at least four Hermitian complex structures. One class
of metrics on $\mathbb{C}H^2$ and all the metrics on $\mathbb{R}H^4$ admit
2spheres of Hermitian complex structures.
The standard metric of $\mathbb{C}H^2$ is the only Einstein metric from the
classification, and also the only metric that admits Kähler structure,
while on $\mathbb{R}H^4$ all the metrics are Einstein. Finally, we examine the
geometry of these Lie groups: curvature properties, selfduality, and holonomy.

343–358 
Almost
additivequadraticcubic mappings in modular spaces.
Mohammad Maghsoudi, Abasalt Bodaghi, Abolfazl Niazi
Motlagh, and Majid Karami
We introduce and obtain the general solution of a class of generalized
mixed additive, quadratic and cubic functional equations. We investigate the
stability of such modified functional equations in the modular space $X_\rho$
by applying the $\Delta_2$condition and the Fatou property (in some results) on
the modular function $\rho$. Furthermore, a counterexample for the even case
(quadratic mapping) is presented.

359–379 
SUSY $N$supergroups and their real forms.
Rita Fioresi and Stephen D. Kwok
We study SUSY $N$supergroups, $N=1,2$, their classification and explicit
realization, together with their real forms. In the end, we give the supergroup
of SUSY preserving automorphisms of $\mathbb{C}^{11}$ and we identify it with a
subsupergroup of the SUSY preserving automorphisms of $\mathbb{P}^{11}$.

381–390 
EtaRicci solitons on LPSasakian manifolds.
Pradip Majhi and Debabrata Kar
We consider $\eta$Ricci solitons on Lorentzian paraSasakian
manifolds with Codazzi type of the Ricci tensor. Then we study $\eta$Ricci
solitons on $\varphi$conformally semisymmetric, $\varphi$Ricci symmetric, and
conformally Ricci semisymmetric Lorentzian paraSasakian manifolds. Finally,
we construct an example of a three dimensional Lorentzian paraSasakian
manifold which admits $\eta$Ricci solitons with nonconstant scalar curvature.

391–405 
Factorization of Frieze patterns.
Moritz Weber and Mang Zhao
In 2017, Michael Cuntz gave a definition of reducibility of a quiddity cycle of
a frieze pattern: It is reducible if it can be written as a sum of two other
quiddity cycles. We discuss the commutativity and associativity of this sum
operator for quiddity cycles and its equivalence classes, respectively.
We show that the sum is neither commutative nor associative, but we may
circumvent this issue by passing to equivalence classes. We also address the
question whether a decomposition of quiddity cycles into irreducible factors is
unique and we answer it in the negative by giving counterexamples. We conclude
that even under stronger assumptions, there is no canonical decomposition.

407–415 
Conformal and Killing vector fields on real submanifolds of the canonical
complex space form $\mathbb{C}^{m}$.
Hanan Alohali, Haila Alodan, and Sharief Deshmukh
In this paper, we find a conformal vector field as well as a Killing vector
field on a compact real submanifold of the canonical complex space form
$\left(\mathbb{C}^{m},J,\left\langle\,,\right\rangle\right)$. In particular,
using immersion $\psi :M\rightarrow\mathbb{C}^{m}$ of a compact real
submanifold $M$ and the complex structure $J$ of the canonical complex space
form $\left(\mathbb{C}^{m},J,\left\langle\,,\right\rangle\right)$, we find
conditions under which the tangential component of $J\psi$ is a conformal
vector field as well as conditions under which it is a Killing vector field.
Finally, we obtain a characterization of $n$spheres in the canonical complex
space form $\left(\mathbb{C}^{m},J,\left\langle\,,\right\rangle\right)$.

417–430 
On $k$circulant
matrices involving the Jacobsthal numbers.
Biljana Radičić
Let $k$ be a nonzero complex number. We consider a $k$circulant matrix whose
first row is $(J_{1},J_{2},\dots,J_{n})$, where $J_{n}$ is the $n^\text{th}$
Jacobsthal number, and obtain the formulae for the eigenvalues of such matrix
improving the formula which can be obtained from the result of Y. Yazlik and
N. Taskara [J. Inequal. Appl. 2013, 2013:394, Theorem 7]. The
obtained formulae for the eigenvalues of a $k$circulant matrix involving the
Jacobsthal numbers show that the result of Z. Jiang, J. Li, and N. Shen
[WSEAS Trans. Math. 12 (2013), no. 3, 341–351, Theorem 10]
is not always applicable. The Euclidean norm of such matrix is determined. We
also consider a $k$circulant matrix whose first row is
$(J_{1}^{1},J_{2}^{1},\dots,J_{n}^{1})$ and obtain the upper and lower
bounds for its spectral norm.

431–442 
Existence and uniqueness
of solutions to distributional differential equations involving
Henstock–Kurzweil–Stieltjes integrals.
Guoju Ye, Mingxia Zhang, Wei Liu, and Dafang Zhao
This paper is concerned with the existence and uniqueness of
solutions to the second order distributional differential equation
with Neumann boundary value problem via Henstock–Kurzweil–Stieltjes
integrals.The existence of solutions is derived from Schauder's
fixed point theorem, and the uniqueness of solutions is established
by Banach's contraction principle. Finally, two examples are
given to demonstrate the main results.

443–458 
Conformal
semiinvariant Riemannian maps to Kähler manifolds.
Mehmet Akif Akyol and Bayram Şahin
As a generalization of CRsubmanifolds and semiinvariant Riemannian maps, we
introduce conformal semiinvariant Riemannian maps from Riemannian manifolds to
almost Hermitian manifolds. We give nontrivial examples, investigate the
geometry of foliations, and obtain decomposition theorems by using the existence
of conformal Riemannian maps. We also investigate the harmonicity of such maps
and find necessary and sufficient conditions for conformal antiinvariant
Riemannian maps to be totally geodesic.

459–468 
A rigidity result
for Kählerian manifolds endowed with closed conformal vector
fields.
Antonio Caminha
We show that if a connected compact Kählerian surface $M$ with nonpositive
Gaussian curvature is endowed with a closed conformal vector field $\xi$ whose
singular points are isolated, then $M$ is isometric to a flat torus and $\xi$
is parallel. We also consider the case of a connected complete Kählerian
manifod $M$ of complex dimension $n > 1$ and endowed with a nontrivial closed
conformal vector field $\xi$. In this case, it is well known that the
singularities of $\xi$ are automatically isolated and the nontrivial leaves of
the distribution generated by $\xi$ and $J\xi$ are totally geodesic in $M$.
Assuming that one such leaf is compact, has torsion normal holonomy group and
that the holomorphic sectional curvature of $M$ along it is nonpositive, we
show that $\xi$ is parallel and $M$ is foliated by a family of totally geodesic
isometric tori and also by a family of totally geodesic isometric complete
Kählerian manifolds of complex dimension $n1$. In particular, the
universal covering of $M$ is isometric to a Riemannian product having
$\mathbb{R}^2$ as a factor. We also comment on a generic class of compact
complex symmetric spaces not possessing nontrivial closed conformal vector
fields, thus showing that we cannot get rid of the hypothesis of nonpositivity
of the holomorphic sectional curvature in the direction of $\xi$.

469–484 
On the mixed integer
randomized pattern search algorithm.
Ebert Brea
We analyze the convergence and performance of a novel direct
search algorithm for identifying at least a local minimum of
unconstrained mixed integer nonlinear optimization problems. The
Mixed Integer Randomized Pattern Search Algorithm (MIRPSA),
socalled by the author, is based on a randomized pattern search,
which is modified by two main operations for finding at least a
local minimum of our problem, namely: moving operation and
shrinking operation. The convergence properties of the MIRPSA are
here analyzed from a Markov chain viewpoint, which is represented
by an infinite countable set of states $\{d(q)\}_{q=0}^{\infty}$,
where each state $d(q)$ is defined by a measure of the $q$th
randomized pattern search $\mathcal{H}_{q}$, for all
$q\in\mathbb{N}$. According to the algorithm, when a moving
operation is carried out on a $q$th randomized pattern
search $\mathcal{H}_{q}$, the MIRPSA Markov chain holds its state.
Meanwhile, if the MIRPSA carries out a shrinking operation on a
$q$th randomized pattern search $\mathcal{H}_{q}$, the
algorithm will then visit the next $(q+1)$th state. Since
the MIRPSA Markov chain never goes back to any visited state, we
therefore say that the MIRPSA yields a birth and miscarriage
Markov chain.

485–503 
Real
hypersurfaces in complex Grassmannians of rank two with semiparallel
structure Jacobi operator.
Avik De, TeeHow Loo, and Changhwa Woo
We prove that there does not exist any real hypersurface in complex
Grassmannians of rank two with semiparallel structure Jacobi operator. With
this result, the nonexistence of real hypersurfaces in complex Grassmannians of
rank two with recurrent structure Jacobi operator is proved.

505–515 
Pseudoholomorphic curves in $\mathbb{S}^6$ and $\mathbb{S}^5$.
JostHinrich Eschenburg and Theodoros Vlachos
The octonionic cross product on $\mathbb{R}^7$ induces a nearly Kähler structure on
$\mathbb{S}^6$, the analogue of the Kähler structure of $\mathbb{S}^2$ given by the usual
(quaternionic) cross product on $\mathbb{R}^3$. Pseudoholomorphic curves with respect
to this structure are the analogue of meromorphic functions. They are
(super)conformal minimal immersions. We reprove a theorem of Hashimoto
[Tokyo J. Math. 23 (2000), 137–159] giving an intrinsic characterization of
pseudoholomorphic curves in
$\mathbb{S}^6$ and (beyond Hashimoto's work) $\mathbb{S}^5$. Instead of the Maurer–Cartan
equations we use an embedding theorem into homogeneous spaces (here: $\mathbb{S}^6 =
G_2/SU_3$) involving the canonical connection.

517–537 
Regularity of maximal functions
associated to a critical radius function.
Bruno Bongioanni, Adrián Cabral, and Eleonor Harboure
In this work we obtain boundedness on BMO and Lipschitz type spaces in the
context of a critical radius function. We deal with a local maximal operator
and a maximal operator of a one parameter family of operators with certain
conditions on its kernels that can be applied to the maximal of the semigroup
in the context of a Schrödinger operator.

539–566 
New extensions
of Cline's formula for generalized Drazin–Riesz inverses.
Abdelaziz Tajmouati, Mohammed Karmouni, and M. B. Mohamed Ahmed
In this note, Cline's formula for generalized Drazin–Riesz inverses is
proved. We prove that if $A, D \in \mathcal{B}(X, Y)$ and $B, C \in
\mathcal{B} (Y, X)$ are such that $ACD =DBD$ and $DBA = ACA$, then $AC$ is
generalized Drazin–Riesz invertible if and only if $BD$ is generalized
Drazin–Riesz invertible, and that, in such a case, if $S$ is a generalized
Drazin–Riesz inverse of $AC$ then $T := BS^2D$ is a generalized Drazin–Riesz
inverse of $BD$.

567–572 
Matrix moment
perturbations and the inverse Szegő matrix transformation.
Edinson Fuentes and Luis E. Garza
Given a perturbation of a matrix measure supported on the unit circle, we
analyze the perturbation obtained on the corresponding matrix measure on the
real line, when both measures are related through the Szegő matrix
transformation. Moreover, using the connection formulas for the corresponding
sequences of matrix orthogonal polynomials, we deduce several properties such
as relations between the corresponding norms. We illustrate the
obtained results with an example.

573–593 
Biconservative Lorentz
hypersurfaces in $\mathbb{E}_{1}^{n+1}$ with complex eigenvalues.
Ram Shankar Gupta and Ahmad Sharfuddin
We prove that every biconservative Lorentz hypersurface $M_{1}^{n}$ in
$\mathbb{E}_{1}^{n+1}$ having complex eigenvalues has constant mean curvature.
Moreover, every biharmonic Lorentz hypersurface $M_{1}^{n}$ having complex
eigenvalues in $\mathbb{E}_{1}^{n+1}$ must be minimal. Also, we provide some
examples of such hypersurfaces.

595–610 
Functional
analytic issues in $\mathbb{Z}_2^n$geometry.
Andrew James Bruce and Norbert Poncin
We show that the function sheaf of a $\mathbb{Z}_2^n$manifold is a nuclear
Fréchet sheaf of $\mathbb{Z}_2^n$graded $\mathbb{Z}_2^n$commutative
associative unital algebras. Further, we prove that the components of the
pullback sheaf morphism of a $\mathbb{Z}_2^n$morphism are all continuous.
These results are essential for the existence of categorical products in the
category of $\mathbb{Z}_2^n$manifolds. All proofs are selfcontained and
explicit.

611–636 
Computing convex
hulls of trajectories.
Daniel Ciripoi, Nidhi Kaihnsa, Andreas Löhne, and
Bernd Sturmfels
We study the convex hulls of trajectories of polynomial dynamical systems.
Such trajectories include real algebraic curves. The boundaries of the
resulting convex bodies are stratified into families of faces. We present
numerical algorithms for identifying these patches. An implementation based on
the software Bensolve Tools is given. This furnishes a key step in computing
attainable regions of chemical reaction networks.

637–662 
