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Journal articles on the topic 'Cartesian product.Mathematics Subject Classification[2000]'

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Published: 3 June 2025

Last updated: 23 June 2025

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1

Lončar, Ivan. "Hereditarily Irreducible Mappings of Cartesian Product of Continua." Sarajevo Journal of Mathematics 7, no. 1 (2024): 115–21. http://dx.doi.org/10.5644/sjm.07.1.11.

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In Section 2 we shall prove that if Cartesian product $X\times Y$ of nondegenerate continua admits a hereditarily irreducible mapping $f:X\times Y\rightarrow Z,$ then w$(X\times Y)$=w$(Z)$. The main section of the paper, Section 3, contains theorems concerning the Whitney maps on continua. In particular, it is proved that the product $\Pi \{X_{s}:s\in S\}$ of nondegenerate continua admits a Whitney map for $C(\Pi \{X_{s}:s\in S\})$ if and only if it is metrizable. 2000 Mathematics Subject Classification. Primary 54B20, 54F15

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2

Şahin, Bayram. "Warped Product Lightlike Submanifolds." Sarajevo Journal of Mathematics 1, no. 2 (2024): 251–60. http://dx.doi.org/10.5644/sjm.01.2.10.

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e study a new class of lightlike submanifolds $M$, called warped product lightlike submanifolds, of a semi-Riemann manifold. We show that the null geometry of $M$ reduces to the corresponding non-degenerate geometry of its semi-Riemann submanifold. 2000 Mathematics Subject Classification. 53C15, 53C40, 53C50

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3

Farsi, Carla. "SOFT C*-ALGEBRAS." Proceedings of the Edinburgh Mathematical Society 45, no. 1 (2002): 59–65. http://dx.doi.org/10.1017/s0013091500000547.

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AbstractIn this paper we consider soft group and crossed product $C^*$-algebras. In particular we show that soft crossed product $C^*$-algebras are isomorphic to classical crossed product $C^*$-algebras. We also prove that large classes of soft $C^*$-algebras have stable rank equal to infinity.AMS 2000 Mathematics subject classification: Primary 46L80; 46L55

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4

Dragomir, S. S. "Power Inequalities for the Numerical Radius of a Product of Two Operators in Hilbert Spaces." Sarajevo Journal of Mathematics 5, no. 2 (2024): 269–78. http://dx.doi.org/10.5644/sjm.05.2.10.

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Some power inequalities for the numerical radius of a product of two operators in Hilbert spaces with applications for commutators and self-commutators are given. 2000 Mathematics Subject Classification. 47A12, 47A30, 47A63, 47B15

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5

du Sautoy, Marcus. "ZETA FUNCTIONS OF GROUPS: EULER PRODUCTS AND SOLUBLE GROUPS." Proceedings of the Edinburgh Mathematical Society 45, no. 1 (2002): 149–54. http://dx.doi.org/10.1017/s0013091500000456.

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AbstractThe well-behaved Sylow theory for soluble groups is exploited to prove an Euler product for zeta functions counting certain subgroups in pro-soluble groups. This generalizes a result of Grunewald, Segal and Smith for nilpotent groups.AMS 2000 Mathematics subject classification: Primary 20F16; 11M99

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6

Diviccaro, Maria Luigia. "Fixed Point Properties of Decomposable Isotone Operators in Posets." Sarajevo Journal of Mathematics 1, no. 1 (2024): 3–7. http://dx.doi.org/10.5644/sjm.01.1.01.

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A known theorem of R. M. Dacić, involving increasing operators decomposable into a finite product of monotone mappings, is extended from a complete lattice to a poset by using our previous results. 2000 Mathematics Subject Classification. 47H10

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7

Kumar, Ajay. "INVOLUTION AND THE HAAGERUP TENSOR PRODUCT." Proceedings of the Edinburgh Mathematical Society 44, no. 2 (2001): 317–22. http://dx.doi.org/10.1017/s0013091599000772.

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AbstractWe show that the involution $\theta(a\otimes b)=a^*\otimes b^*$ on the Haagerup tensor product $A\otimes_{\mrm{H}}B$ of $C^*$-algebras $A$ and $B$ is an isometry if and only if $A$ and $B$ are commutative. The involutive Banach algebra $A\otimes_{\mrm{H}}A$ arising from the involution $a\otimes b\to b^*\otimes a^*$ is also studied.AMS 2000 Mathematics subject classification: Primary 46L05; 46M05

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8

Shwartz, Robert. "ON THE FREIHEITSSATZ IN CERTAIN ONE-RELATOR FREE PRODUCTS. III." Proceedings of the Edinburgh Mathematical Society 45, no. 3 (2002): 693–700. http://dx.doi.org/10.1017/s0013091599001224.

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AbstractWe study one-relator free products in which the relator has free-product length $4$. We find conditions for such presentations to have a Freiheitssatz and classify all non-aspherical presentations under certain conditions.AMS 2000 Mathematics subject classification: Primary 20F05; 20F06; 20F10

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9

Fisher, Brian, E. Öz¸ça, and Ü. Gülen. "A Theorem on the Commutative Neutrix Product of Distributions." Sarajevo Journal of Mathematics 1, no. 2 (2024): 235–42. http://dx.doi.org/10.5644/sjm.01.2.08.

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The commutative neutrix products $f_+(x) \cdot \delta ^{(r)}(x)$ and $f_-(x)$ $\cdot \delta ^{(r)}(x) $ are evaluated for $r=0,1,2,\ldots,$ where $f$ is a function which is infinitely differentiable on an open interval containing the origin and $f_+(x) =H(x)f(x)$ and $f_-(x) =H(-x)f(x),$ $H$ denoting Heaviside's function. 2000 Mathematics Subject Classification. 46F10

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10

Faĭziev, Valeriy A., and Prasanna K. Sahoo. "Remark on the Second Bounded Cohomology of Amalgamated Product of Groups." Sarajevo Journal of Mathematics 1, no. 1 (2024): 27–48. http://dx.doi.org/10.5644/sjm.01.1.05.

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For any cardinal number ${\mathcal M}$ we construct examples of amalgamated products and HNN extensions of groups such that the dimension of the space of second bounded cohomologies is at least ${\mathcal M}$. Also we describe the space of pseudocharacters of the group $GL(2,F_2[z]).$ 2000 Mathematics Subject Classification. Primary: 20M15, 20M30, 39B82

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11

Fisher, Brian, Inci Ege, and Emin Özçag. "On the Non-commutative Neutrix Product of the Distributions $\delta ^{(r)}(x)$ and $x^{-s}\ln^m|x|$}." Sarajevo Journal of Mathematics 2, no. 2 (2024): 211–21. http://dx.doi.org/10.5644/sjm.02.2.08.

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It is proved that the non-commutative neutrix product of the distributions $ \delta ^{(r)}(x)$ and $x^{-s} \ln^m|x|$ exists and $$ \delta ^{(r)}(x) \circ x^{-s} \ln^m |x| = 0 $$ for $r,m=0,1,2, \ldots$ and $s = 1,2, \ldots.$ 2000 Mathematics Subject Classification. 46F10

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12

Atani, S. Ebrahimi, and M. Shajari Kohan. "The Diameter of a Zero-Divisor Graph for Finite Direct Product of Commutative Rings." Sarajevo Journal of Mathematics 3, no. 2 (2024): 149–56. http://dx.doi.org/10.5644/sjm.03.2.01.

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This paper establishes a set of theorems that describe the diameter of a zero-divisor graph for a finite direct product$R_{1}\times R_{2}\times\cdots\times R_{n}$ with respect to the diameters of the zero-divisor graphs of $R_{1},R_{2},\cdots,R_{n-1}$ and $R_{n}(n>2).$ 2000 Mathematics Subject Classification. 05C75, 13A15

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13

Blyth, Russell D., Robert Fitzgerald Morse, and Joanne L. Redden. "ON COMPUTING THE NON-ABELIAN TENSOR SQUARES OF THE FREE 2-ENGEL GROUPS." Proceedings of the Edinburgh Mathematical Society 47, no. 2 (2004): 305–23. http://dx.doi.org/10.1017/s0013091502000998.

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AbstractIn this paper we compute the non-abelian tensor square for the free 2-Engel group of rank $n>3$. The non-abelian tensor square for this group is a direct product of a free abelian group and a nilpotent group of class 2 whose derived subgroup has exponent 3. We also compute the non-abelian tensor square for one of the group’s finite homomorphic images, namely, the Burnside group of rank $n$ and exponent 3.AMS 2000 Mathematics subject classification: Primary 20F05; 20F45. Secondary 20F18

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14

Paulsen, Vern I., and Roger R. Smith. "DIAGONALS IN TENSOR PRODUCTS OF OPERATOR ALGEBRAS." Proceedings of the Edinburgh Mathematical Society 45, no. 3 (2002): 647–52. http://dx.doi.org/10.1017/s0013091500001073.

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AbstractIn this paper we give a short, direct proof, using only properties of the Haagerup tensor product, that if an operator algebra $A$ possesses a diagonal in the Haagerup tensor product of $A$ with itself, then $A$ must be isomorphic to a finite-dimensional $C^*$-algebra. Consequently, for operator algebras, the first Hochschild cohomology group $H^1(A,X)=0$ for every bounded, Banach $A$-bimodule $X$, if and only if $A$ is isomorphic to a finite-dimensional $C^*$-algebra.AMS 2000 Mathematics subject classification: Primary 46L06. Secondary 46L05

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15

Muratović, Amela. "Representation of Polynomials Over Finite Fields With Circulants." Sarajevo Journal of Mathematics 1, no. 1 (2024): 21–26. http://dx.doi.org/10.5644/sjm.01.1.04.

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Representation of polynomials over complex fields is well known. In this paper a similar representation is given for polynomials of degree less than $q-1$, over finite fields. The results are theorems that characterize the centralizer of the circulant of a permutation polynomial, and a formula for the calculation of the determinant of the circulant as the product of the determinants of the polynomials defined on the cosets of some multilpicative subgroup. 2000 Mathematics Subject Classification. 12E05, 16S50

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16

Nadler, Jr., Sam B. "Pointwise Products of Uniformly Continuous Functions." Sarajevo Journal of Mathematics 1, no. 1 (2024): 117–27. http://dx.doi.org/10.5644/sjm.01.1.10.

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The problem of characterizing the metric spaces on which the pointwise product of any two uniformly continuous real - valued functions is uniformly continuous is investigated. A sufficient condition is given; furthermore, the condition is shown to be necessary for certain types of metric spaces, which include those with no isolated point and all subspaces of Euclidean spaces. It is not known if the condition is always necessary. 2000 Mathematics Subject Classification. Primary: 54C10, 54C30; Secondary: 20M20

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17

Deicke, Klaus. "THE CROSSED PRODUCT BY A POINTWISE UNITARY ACTION ON A C*-ALGEBRA WITH CONTINUOUS TRACE." Proceedings of the Edinburgh Mathematical Society 44, no. 1 (2001): 215–18. http://dx.doi.org/10.1017/s0013091500000195.

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AbstractLet $G$ be a locally compact group, $A$ a continuous trace $C^*$-algebra, and $\alpha$ a pointwise unitary action of $G$ on $A$. It is a result of Olesen and Raeburn that if $A$ is separable and $G$ is second countable, then the crossed product $A\times_\alpha G$ has continuous trace. We present a new and much more elementary proof of this fact. Moreover, we do not even need the separability assumptions made on $A$ and $G$.AMS 2000 Mathematics subject classification: Primary 46L55

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18

Baaj, Saad, and Stefaan Vaes. "DOUBLE CROSSED PRODUCTS OF LOCALLY COMPACT QUANTUM GROUPS." Journal of the Institute of Mathematics of Jussieu 4, no. 1 (2005): 135–73. http://dx.doi.org/10.1017/s1474748005000034.

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For a matched pair of locally compact quantum groups, we construct the double crossed product as a locally compact quantum group. This construction generalizes Drinfeld’s quantum double construction. We study the modular theory and the $\mathrm{C}^*$-algebraic properties of these double crossed products, as well as several links between double crossed products and bicrossed products. In an appendix, we study the Radon–Nikodym derivative of a weight under a quantum group action (following Yamanouchi) and obtain, as a corollary, a new characterization of closed quantum subgroups. AMS 2000 Mathematics subject classification: Primary 46L89. Secondary 46L65

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19

Aichinger, Erhard. "ON NEAR-RING IDEMPOTENTS AND POLYNOMIALS ON DIRECT PRODUCTS OF Ω-GROUPS". Proceedings of the Edinburgh Mathematical Society 44, № 2 (2001): 379–88. http://dx.doi.org/10.1017/s0013091599001418.

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AbstractLet $N$ be a zero-symmetric near-ring with identity, and let $\sGa$ be a faithful tame $N$-group. We characterize those ideals of $\sGa$ that are the range of some idempotent element of $N$. Using these idempotents, we show that the polynomials on the direct product of the finite $\sOm$-groups $V_1,V_2,\dots,V_n$ can be studied componentwise if and only if $\prod_{i=1}^nV_i$ has no skew congruences.AMS 2000 Mathematics subject classification: Primary 16Y30. Secondary 08A40

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20

Chen, Bang-Yen. "ON ISOMETRIC MINIMAL IMMERSIONS FROM WARPED PRODUCTS INTO REAL SPACE FORMS." Proceedings of the Edinburgh Mathematical Society 45, no. 3 (2002): 579–87. http://dx.doi.org/10.1017/s001309150100075x.

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AbstractWe establish a general sharp inequality for warped products in real space form. As applications, we show that if the warping function $f$ of a warped product $N_1\times_fN_2$ is a harmonic function, then(1) every isometric minimal immersion of $N_1\times_fN_2$ into a Euclidean space is locally a warped-product immersion, and(2) there are no isometric minimal immersions from $N_1\times_f N_2$ into hyperbolic spaces.Moreover, we prove that if either $N_1$ is compact or the warping function $f$ is an eigenfunction of the Laplacian with positive eigenvalue, then $N_1\times_f N_2$ admits no isometric minimal immersion into a Euclidean space or a hyperbolic space for any codimension. We also provide examples to show that our results are sharp.AMS 2000 Mathematics subject classification: Primary 53C40; 53C42; 53B25

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21

Fisher, Brian. "Two Results on the Commutative Product of Distributions and Functions." Sarajevo Journal of Mathematics 6, no. 1 (2024): 81–87. http://dx.doi.org/10.5644/sjm.06.1.07.

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Let $f$ and $g$ be distributions and let $f_n=(f*\delta_n x)$ and $g_n =(g*\delta _n)(x)$, where $\delta _n(x)$ is a certain sequence converging to the Dirac delta-function. The product $f .g$ of $f$ and $g$ is defined to be the limit of the sequence $\{f_ng_n\}$, provided its limit $h$ exists in the sense that $$\lim _{n \to \infty} \langle f_n (x) g_n (x),\vphi (x) \rangle =\langle h(x), \vphi (x) \rangle $$ for all functions $\vphi$ in ${\mathcal D}.$ It is proved that \begin{align*}(\sgn x|x| ^{-r} \ln ^p |x|). ( |x| ^\mu \ln^q|x|)&=\sgn x |x| ^{-r +\mu } \ln ^{p+q}|x| ,\\(|x| ^{-r} \ln ^p |x|). (\sgn x |x| ^\mu \ln ^q|x| ) &=\sgn x |x| ^{-r +\mu } \ln ^{p+q}|x|\end{align*}for $-2<-r+\mu< -1,$ $r=1,2, \ldots$ and $p,q =0,1,2. \ldots .$ 2000 Mathematics Subject Classification. 46F10

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22

Crossley, M. D., and Sarah Whitehouse. "HIGHER CONJUGATION COHOMOLOGY IN COMMUTATIVE HOPF ALGEBRAS." Proceedings of the Edinburgh Mathematical Society 44, no. 1 (2001): 19–26. http://dx.doi.org/10.1017/s0013091599000826.

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AbstractLet $A$ be a graded, commutative Hopf algebra. We study an action of the symmetric group $\sSi_n$ on the tensor product of $n-1$ copies of $A$; this action was introduced by the second author in 1 and is relevant to the study of commutativity conditions on ring spectra in stable homotopy theory 2.We show that for a certain class of Hopf algebras the cohomology ring $H^*(\sSi_n;A^{\otimes n-1})$ is independent of the coproduct provided $n$ and $(n-2)!$ are invertible in the ground ring. With the simplest coproduct structure, the group action becomes particularly tractable and we discuss the implications this has for computations.AMS 2000 Mathematics subject classification: Primary 16W30; 57T05; 20C30; 20J06; 55S25

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23

Achilles, Rüdiger, and Mirella Manaresi. "SELF-INTERSECTIONS OF SURFACES AND WHITNEY STRATIFICATIONS." Proceedings of the Edinburgh Mathematical Society 46, no. 3 (2003): 545–59. http://dx.doi.org/10.1017/s0013091503000026.

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AbstractLet $X$ be a surface in $\mathbb{C}^n$ or $\mathbb{P}^n$ and let $C_{X}(X\times X)$ be the normal cone to $X$ in $X\times X$ (diagonally embedded). For a point $x\in X$, denote by $g(x):=e_x(C_X(X\times X))$ the multiplicity of $C_X(X\times X)$ at $x$. It is a former result of the authors that $g(x)$ is the degree at $x$ of the Stückrad–Vogel cycle $v(X,X)=\sum_C j(X,X;C)[C]$ of the self-intersection of $X$, that is, $g(x)=\sum_Cj(X,X;C)e_x(C)$. We prove that the stratification of $X$ by the multiplicity $g(x)$ is a Whitney stratification, the canonical one if $n=3$. The corresponding result for hypersurfaces in $\mathbb{A}^n$ or $\mathbb{P}^n$, diagonally embedded in a multiple product with itself, was conjectured by van Gastel. This is also discussed, but remains open.AMS 2000 Mathematics subject classification: Primary 32S15. Secondary 13H15;14C17

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24

BRAVO, A., and O. VILLAMAYOR U. "A STRENGTHENING OF RESOLUTION OF SINGULARITIES IN CHARACTERISTIC ZERO." Proceedings of the London Mathematical Society 86, no. 2 (2003): 327–57. http://dx.doi.org/10.1112/s0024611502013801.

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Let $X$ be a closed subscheme embedded in a scheme $W$, smooth over a field ${\bf k}$ of characteristic zero, and let ${\mathcal I} (X)$ be the sheaf of ideals defining $X$. Assume that the set of regular points of $X$ is dense in $X$. We prove that there exists a proper, birational morphism, $\pi : W_r \longrightarrow W$, obtained as a composition of monoidal transformations, so that if $X_r \subset W_r$ denotes the strict transform of $X \subset W$ then:(1) the morphism $\pi : W_r \longrightarrow W$ is an embedded desingularization of $X$ (as in Hironaka's Theorem);(2) the total transform of ${\mathcal I} (X)$ in ${\mathcal O}_{W_r}$ factors as a product of an invertible sheaf of ideals ${\mathcal L}$ supported on the exceptional locus, and the sheaf of ideals defining the strict transform of $X$ (that is, ${\mathcal I}(X){\mathcal O}_{W_r} = {\mathcal L} \cdot {\mathcal I}(X_r)$).Thus (2) asserts that we can obtain, in a simple manner, the equations defining the desingularization of $X$.2000 Mathematical Subject Classification: 14E15.

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25

Popescu, Gelu. "!COMMUTANT LIFTING, TENSOR ALGEBRAS, AND FUNCTIONAL CALCULUS." Proceedings of the Edinburgh Mathematical Society 44, no. 2 (2001): 389–406. http://dx.doi.org/10.1017/s0013091598001059.

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AbstractA non-commutative multivariable analogue of Parrott’s generalization of the Sz.-Nagy–Foia\c{s} commutant lifting theorem is obtained. This yields Tomita-type commutant results and interpolation theorems (e.g. Sarason, Nevanlinna–Pick, Carathéodory) for $F_n^\infty\,\bar{\otimes}\,\M$, the weakly-closed algebra generated by the spatial tensor product of the non-commutative analytic Toeplitz algebra $F_n^\infty$ and an arbitrary von Neumann algebra $\M$. In particular, we obtain interpolation theorems for bounded analytic functions from the open unit ball of $\mathbb{C}^n$ into a von Neumann algebra.A variant of the non-commutative Poisson transform is used to extend the von Neumann inequality to tensor algebras, and to provide a generalization of the functional calculus for contractive sequences of operators on Hilbert spaces. Commutative versions of these results are also considered.AMS 2000 Mathematics subject classification: Primary 47L25; 47A57; 47A60. Secondary 30E05

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26

Groves, James S. "ORNSTEIN–UHLENBECK PROCESSES IN BANACH SPACES AND THEIR SPECTRAL REPRESENTATIONS." Proceedings of the Edinburgh Mathematical Society 45, no. 2 (2002): 301–25. http://dx.doi.org/10.1017/s0013091500001231.

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AbstractFor Q the variance of some centred Gaussian random vector in a separable Banach space it is shown that, necessarily, Q factors through $\ell^2$ as a product of 2-summing operators. This factorization condition is sufficient when the Banach space is of Gaussian type 2. The stochastic integral of a deterministic family of operators with respect to a Q-Wiener process is shown to exist under a continuity condition involving the 2-summing norm. A Langevin equation$$ \rd\bm{Z}_t+\sLa\bm{Z}_t\,\rd t=\rd\bm{B}_t, $$with values in a separable Banach space, is studied. The operator $\sLa$ is closed and densely defined. A weak solution $(\bm{Z}_t,\bm{B}_t)$, where $\bm{Z}_t$ is centred, Gaussian and stationary, while $\bm{B}_t$ is a Q-Wiener process, is given when $\ri\sLa$ and $\ri\sLa^*$ generate $C_0$ groups and the resolvent of $\sLa$ is uniformly bounded on the imaginary axis. Both $\bm{Z}_t$ and $\bm{B}_t$ are stochastic integrals with respect to a spectral Q-Wiener process.AMS 2000 Mathematics subject classification: Primary 60G15. Secondary 46E40; 47B10; 47D03; 60H10

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27

Akinola, Lukman Shina. "On the action of a fuzzy group on a fuzzy set." Fountain Journal of Natural and Applied Sciences 12, no. 1 (2023). http://dx.doi.org/10.53704/fujnas.v12i1.445.

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In this paper, we develop fundamental concepts required to extend the concept of group action on a set to fuzzy domain. We define product of a fuzzy set and a fuzzy group by using the idea of cartesian products of sets. We construct examples to demonstrate the defined concepts. We also discuss properties of the defined product of a fuzzy set and a fuzzy group as requisite to study of fuzzy group actions on fuzzy sets. Mathematics Subject Classification (2020). 08A99, 08C05, 22F05

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28

S.K., Sardar, Mandal D. та Mukherjee R. "A Study on Intuitionistic Fuzzy h-ideal in Γ-Hemirings". 25 серпня 2011. https://doi.org/10.5281/zenodo.1055072.

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The notions of intuitionistic fuzzy h-ideal and normal intuitionistic fuzzy h-ideal in Γ-hemiring are introduced and some of the basic properties of these ideals are investigated. Cartesian product of intuitionistic fuzzy h-ideals is also defined. Finally a characterization of intuitionistic fuzzy h-ideals in terms of fuzzy relations is obtained.

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