Search results for " Mathematica"
showing 10 items of 689 documents
Spectrum of composition operators on S(R) with polynomial symbols
2020
Abstract We study the spectrum of operators in the Schwartz space of rapidly decreasing functions which associate each function with its composition with a polynomial. In the case where this operator is mean ergodic we prove that its spectrum reduces to {0}, while the spectrum of any non mean ergodic composition operator with a polynomial always contains the closed unit disc except perhaps the origin. We obtain a complete description of the spectrum of the composition operator with a quadratic polynomial or a cubic polynomial with positive leading coefficient.
Trace identities and almost polynomial growth
2021
In this paper we study algebras with trace and their trace polynomial identities over a field of characteristic 0. We consider two commutative matrix algebras: $D_2$, the algebra of $2\times 2$ diagonal matrices and $C_2$, the algebra of $2 \times 2$ matrices generated by $e_{11}+e_{22}$ and $e_{12}$. We describe all possible traces on these algebras and we study the corresponding trace codimensions. Moreover we characterize the varieties with trace of polynomial growth generated by a finite dimensional algebra. As a consequence, we see that the growth of a variety with trace is either polynomial or exponential.
Varieties of special Jordan algebras of almost polynomial growth
2019
Abstract Let J be a special Jordan algebra and let c n ( J ) be its corresponding codimension sequence. The aim of this paper is to prove that in case J is finite dimensional, such a sequence is polynomially bounded if and only if the variety generated by J does not contain U J 2 , the special Jordan algebra of 2 × 2 upper triangular matrices. As an immediate consequence, we prove that U J 2 is the only finite dimensional special Jordan algebra that generates a variety of almost polynomial growth.
Rainwater Reuse in Urban Areas: A Mathematical Model and a Long-Term Modelling Approach
2018
Natural water resources are becoming increasingly limited due to global-scale climate change and water availability issues have become so severe that they must be addressed. Given these issues, reuse of wastewater and rainwater provides a promising way to cope with water shortages. This paper describes an investigation into the efficiency of rainwater usage systems. A conceptual model was built to assess the behaviour of rainwater tanks and their effectiveness in coping with water shortages. The study is based on a long-term simulation (12 years) of different rainwater reuse tank schemes. The associated reductions in residential freshwater demand (water reuse efficiency) and wet-weather run…
Zeros of {-1,0,1}-power series and connectedness loci for self-affine sets
2006
We consider the set W of double zeros in (0,1) for power series with coefficients in {-1,0,1}. We prove that W is disconnected, and estimate the minimum of W with high accuracy. We also show that [2^(-1/2)-e,1) is contained in W for some small, but explicit e>0 (this was only known for e=0). These results have applications in the study of infinite Bernoulli convolutions and connectedness properties of self-affine fractals.
$V$-filtrations in positive characteristic and test modules
2013
Let $R$ be a ring essentially of finite type over an $F$-finite field. Given an ideal $\mathfrak{a}$ and a principal Cartier module $M$ we introduce the notion of a $V$-filtration of $M$ along $\mathfrak{a}$. If $M$ is $F$-regular then this coincides with the test module filtration. We also show that the associated graded induces a functor $Gr^{[0,1]}$ from Cartier crystals to Cartier crystals supported on $V(\mathfrak{a})$. This functor commutes with finite pushforwards for principal ideals and with pullbacks along essentially \'etale morphisms. We also derive corresponding transformation rules for test modules generalizing previous results by Schwede and Tucker in the \'etale case (cf. ar…
Análisis de la adecuación de libros de texto de E. Primaria a la enseñanza a estudiantes de altas capacidades matemáticas
2013
Un problema al que se enfrentan los profesores de matemáticas de Enseñanza Primaria es la necesidad de hacer adaptaciones en sus programaciones para ofrecer una educación adecuada a sus alumnos de altas capacidades matemáticas. Las editoriales de libros de texto de matemáticas de estos niveles educativos ofrecen diversas soluciones que, usualmente, consisten en incluir, en el libro del alumno, algunos problemas más difíciles y, en la documentación del profesor, una propuesta de problemas de ampliación. Una cuestión que se plantea al analizar un libro de texto de matemáticas es valorar cómo de útil puede ser el material proporcionado por la editorial (libro de texto y materiales complementar…
Empirical Likelihood Method for a Location Parameter Using Some Robust Estimators
2022
Pētījumā attīstītas empīriskās ticamības (EL) metodes divu un vairāku neatkarīgu populāciju salīdzināšanai, balstoties uz robustiem lokācijas parametra novērtētājiem. Iegūti jauni asimptotiskie rezultāti par empīriskās ticamības metodēm: 1) divu M-novērtētāju starpībai; 2) divu nošķeltu vidējo vērtību starpībai; 3) uz empīrisko ticamību balstītai ANOVA metodei vairāk kā divu nošķeltu vidējo vērtību salīdzināšanai. Tika izstrādāts simulāciju eksperiments un analizēti datu piemēri, kas parādīja, ka jauniegūtās metodes ir līdzvērtīga alternatīva klasiskās statistikas metodēm gadījumos, kad dati ir normāli sadalīti – tām ir līdzīga jauda un spēja kontrolēt empīrisko pirmā veida kļūdu. Turklāt m…
Productive Ambiguity in Mathematics
2011
According to E. Grosholz, there is a phenomenon called `productive ambiguity' which plays a very important role in mathematics, and the sciences, because it is instrumental to the resolution of many open questions. The main task of this paper is that of assessing Grosholz's claim with regard to mathematics.
Singular quasisymmetric mappings in dimensions two and greater
2018
For all $n \geq 2$, we construct a metric space $(X,d)$ and a quasisymmetric mapping $f\colon [0,1]^n \rightarrow X$ with the property that $f^{-1}$ is not absolutely continuous with respect to the Hausdorff $n$-measure on $X$. That is, there exists a Borel set $E \subset [0,1]^n$ with Lebesgue measure $|E|>0$ such that $f(E)$ has Hausdorff $n$-measure zero. The construction may be carried out so that $X$ has finite Hausdorff $n$-measure and $|E|$ is arbitrarily close to 1, or so that $|E| = 1$. This gives a negative answer to a question of Heinonen and Semmes.