Diogo D. P. S. e Silva

On the upper bounds for the constants of the Hardy–Littlewood inequality☆

Abstract The best known upper estimates for the constants of the Hardy–Littlewood inequality for m-linear forms on l p spaces are of the form ( 2 ) m − 1 . We present better estimates which depend on p and m. An interesting consequence is that if p ≥ m 2 then the constants have a subpolynomial growth as m tends to infinity.

Numerical Simulation of the Water Diffusion in Cylindrical Solids

In this article, a mathematical model was developed for the numerical simulation of the water diffusion in an infinite cylinder. A solver for the diffusion equation was created using the finite volume method, with a fully implicit formulation. In order to create such solver, it was assumed that the boundary condition of the first type is adequate to simulate the physical problem. The solver presupposes variable thermophysical properties and radius in the domain. In order to determine the parameters of the expression between the diffusivity and the moisture content, an optimizer was created, based on the inverse method. The developed mathematical model was applied to simulate the drying of banana and rough rice, using experimental data obtained from the literature. The results obtained in this article, considering the variable diffusivity, are better than the results obtained originally in the literature, where the water diffusivity was considered constant.

''LAB Fit ajuste de curvas'': um software em português para tratamento de dados experimentais

This paper aims to communicate the development of a software for treatment of experimental data called LAB Fit (curve fitting, 2D and 3D graphs, basic statistics, error propagation and mathematical tools). The english version was released two years ago and, due to the achieved success, verified by the great number of downloads, it is also being released a portuguese version. Typical examples of using of the LAB Fit show part of the potentialities of the program in the experimental teaching and research. The performance of the software has been verified with the Statistical Reference Datasets Project (SRDP) of the National Institute of Standards and Technology (NIST), which presents 27 datasets (and functions) with certified values for the parameters. All the 27 LAB Fit results are statistically identical to the certified values.

The Speed of Sound in Air: An At-Home Experiment

This paper describes a simple experiment that students can do at home to determine the speed of sound in air. A set of audio files with selected frequencies is first created and stored on the students computer. Resonances are obtained in a straight pipe partially inserted into a bucket of water. The length of the air-filled part of the pipe is changed by raising and lowering the pipe. Resonances are detected by ear. We present some typical results obtained by students at home. All are in good agreement with the expected value.

On the graded identities for elementary gradings in matrix algebras over infinite fields

We find a basis for the G-graded identities of the n × n matrix algebra Mn(K) over an infinite field K of characteristic p>0 with an elementary grading such that the neutral component corresponds to the diagonal of Mn(K).

Graded identities of block-triangular matrices

Abstract Let F be an infinite field and U T ( d 1 , … , d n ) be the algebra of upper block-triangular matrices over F. In this paper we describe a basis for the G-graded polynomial identities of U T ( d 1 , … , d n ) , with an elementary grading induced by an n-tuple of elements of a group G such that the neutral component corresponds to the diagonal of U T ( d 1 , … , d n ) . In particular, we prove that the monomial identities of such algebra follow from the ones of degree up to 2 n − 1 . Our results generalize, for infinite fields of arbitrary characteristic, previous results in the literature which were obtained for fields of characteristic zero and for particular G-gradings. In the characteristic zero case we also generalize results for the algebra U T ( d 1 , … , d n ) ⊗ C with a tensor product grading, where C is a color commutative algebra generating the variety of all color commutative algebras.

A primeness property for central polynomials of verbally prime P.I. algebras

Let and be two non-commutative polynomials in disjoint sets of variables. An algebra is verbally prime if whenever is an identity for then either or is also an identity. As an analogue of this property, Regev proved that the verbally prime algebra of matrices over an infinite field has the following primeness property for central polynomials: whenever the product is a central polynomial for then both and are central polynomials. In this paper, we prove that over a field of characteristic zero, Regev’ s result holds for the verbally prime algebras and , where is the infinite-dimensional Grassmann algebra.Let and be two non-commutative polynomials in disjoint sets of variables. An algebra is verbally prime if whenever is an identity for then either or is also an identity. As an analogue of this property, Regev proved that the verbally prime algebra of matrices over an infinite field has the following primeness property for central polynomials: whenever the product is a central polynomial for then both and are central polynomials. In this paper, we prove that over a field of characteristic zero, Regev’ s result holds for the verbally prime algebras and , where is the infinite-dimensional Grassmann algebra.

Measurement of specific heat and Newton's law of cooling: a refinement in the analysis of the experimental data

One of the techniques for the determination of the specific heat of solids and liquids use the Newtons law of cooling for the analysis of the experimental data instead of the usual calorimeter method. The success of this technique depends on the possibility in determining the temperatures of the system immediately before and after the internal heat transfer due to the immersion of the sample (whose specific heat one wants to measure) with small uncertainties in a container filled with hot water. In this paper a refinement of this technique is proposed using two curve fittings for the function that describes the law of cooling and small extrapolations to determine those temperatures, as well their uncertainties. This allows to determine not only the value of the specific heat, but also the uncertainty of this value by error propagation. The fitting of the function that describes the law of cooling (and not of polynomials) to the data allows the comparison of the parameters obtained from the experiment with those predicted by the theory, and there is good agreement. The application of this refinement to the determination of the specific heat of aluminium indicates that the procedure is good in spite of the use of low cost apparatus.

Influência da temperatura do ar de secagem no calor latente de vaporização de água em feijão macassar (Vigna unguiculata (L.) Walp.), variedade sempre-verde

In order to determine the energy needed to artificially dry an agricultural product the latent heat of vaporization of moisture in the product, H, must be known. Generally, the expressions for H reported in the literature are of the form H = h(T)f(M), where h(T) is the latent heat of vaporization of free water, and f(M) is a function of the equilibrium moisture content, M, which is a simplification. In this article, a more general expression for the latent heat of vaporization, namely H = g(M,T), is used to determine H for cowpea, always-green variety. For this purpose, a computer program was developed which automatically fits about 500 functions, with one or two independent variables, imbedded in its library to experimental data. The program uses nonlinear regression, and classifies the best functions according to the least reduced chi-squared. A set of executed statistical tests shows that the generalized expression for H used in this work produces better results of H for cowpea than other equations found in literature.

Calculation of the Uncertainty in the Determination of the Equilibrium Moisture Content of Pumpkin Seed Flour

Empiric equations for the determination of the equilibrium moisture content as a function of temperature and relative humidity of air are normally obtained from experimental data by curve fitting. Once the fitting parameters of a function for a given product are determined, the value of that function for specific values of temperature and humidity of air is obtained by substituting these values into the function, which represents an indirect measurement. Generally, the results of these modelings are stated without the uncertainties inherent in the measurement. This article proposes a method for the determination of these uncertainties. For that, a computer code was developed which calculates the error propagation in first order approximation from the obtained fitting parameters and their covariances. The code was used for the determination of the uncertainties of the equilibrium moisture content of pumpkin seed flour, both for adsorption and desorption. This procedure allows a report of the measurement in agreement with the rules established by international standardization organizations.