A simple demonstration of the existence of the jordan canonical form for any square matrix

All the demonstrations known to this author of the existence of the Jordan Canonical Form are somewhat complex - usually invoking the use of new spaces, and what not. These demonstrations are usually too difficult for an average Mathematics student to understand how he or she can obtain the Jordan Canonical Form for any square matrix. The method here proposed not only demonstrates the existence of such forms but, additionally, shows how to find them in a step by step manner. I do not claim that the following demonstration is in any way “elegant” (by the standards of elegance in fashion nowadays among mathematicians) but merely simple (undergraduate students taking a fist course in Matrix Algebra would understand how it works).

Evaluating the existence of structural change in the brazilian term structure of interest: evidence based on cointegration models with structural break

This paper investigates whether there is evidence of structural change in the Brazilian term structure of interest rates. Multivariate cointegration techniques are used to verify this evidence. Two econometrics models are estimated. The rst one is a Vector Autoregressive Model with Error Correction Mechanism (VECM) with smooth transition in the deterministic coe¢ cients (Ripatti and Saikkonen [25]). The second one is a VECM with abrupt structural change formulated by Hansen [13]. Two datasets were analysed. The rst one contains a nominal interest rate with maturity up to three years. The second data set focuses on maturity up to one year. The rst data set focuses on a sample period from 1995 to 2010 and the second from 1998 to 2010. The frequency is monthly. The estimated models suggest the existence of structural change in the Brazilian term structure. It was possible to document the existence of multiple regimes using both techniques for both databases. The risk premium for di¤erent spreads varied considerably during the earliest period of both samples and seemed to converge to stable and lower values at the end of the sample period. Long-term risk premiums seemed to converge to inter-national standards, although the Brazilian term structure is still subject to liquidity problems for longer maturities.

Existence of nash equilibrium in competitive nonlinear pricing games with adverse selection

We show that for a large class of competitive nonlinear pricing games with adverse selection, the property of better-reply security is naturally satisfied - thus, resolving via a result due to Reny (1999) the issue of existence of Nash equilibrium for a large class of competitive nonlinear pricing games.

Dynamics at infinity and the existence of singularly degenerate heteroclinic cycles in the Lorenz system

In this paper, by using the Poincare compactification in R(3) we make a global analysis of the Lorenz system, including the complete description of its dynamic behavior on the sphere at infinity. Combining analytical and numerical techniques we show that for the parameter value b = 0 the system presents an infinite set of singularly degenerate heteroclinic cycles, which consist of invariant sets formed by a line of equilibria together with heteroclinic orbits connecting two of the equilibria. The dynamical consequences related to the existence of such cycles are discussed. In particular a possibly new mechanism behind the creation of Lorenz-like chaotic attractors, consisting of the change in the stability index of the saddle at the origin as the parameter b crosses the null value, is proposed. Based on the knowledge of this mechanism we have numerically found chaotic attractors for the Lorenz system in the case of small b > 0, so nearby the singularly degenerate heteroclinic cycles.

Electronic spectra, ESR and crystal structure of tetrahedral halocuprates(II). The existence of cations (2tbpo·H+) with a very short hydrogen bond

Two compounds [2tbpo·H+)2[CuCl4]= (yellow) and (2tbpo·H+)2[CuBr4]= (dark purple) (tbpo = tribenzylphosphine oxide) have been prepared and investigated by means of crystal structure, electronic, vibrational and ESR spectra. The crystal structure of the (2tbpo·H+)2[CuCl4]= complex was determined by three-dimensional X-ray diffraction. The compound crystallizes in the space group P42/n with unit-cell dimensions a = 19.585(2), c = 9.883(1)Å, V = 3790 (1)Å3, Z = 2, Dm = 1.303 (flotation) Dx = 1.302 Mg m-3. The structure was solved by direct methods and refined by blocked full-matrix least-squares to R = 0.053 for 2583 observed reflections. Cu(II) is coordinated to four chlorides in a tetrahedral arrangement. Tribenzylphosphine oxide molecules, related by a centre of inversion, are connected by a short hydrogen bridge. Chemical analysis, electronic and vibrational spectra showed that the bromide compound is similar to the chloride one and can be formulated as (2tbpo·H+)2[CuBr4]=. The position of the dd transition bands, the charge transfer bands, the ESR and the vibrational spectra of both complexes are discussed. The results are compared with analogous complexes cited in the literature. © 1983.

Existence of Lagrangians for the Yang-Mills equations

The Yang-Mills equations only admit a Lagrangian for gauge groups which are either semisimple or Abelian, or a direct product of groups of both kinds. © 1988.

Decay of accelerated protons and the existence of the Fulling-Davies-Unruh effect

A theoretic-oriented strategy was taken to address the weak decay of uniformly accelerated protons. The decay of uniformly accelerated p+'s was analyzed using standard quantum field theory (QFT). It was shown that the FDU effect is essential to reproduce the proper decay rate in the uniformly accelerated frame.

On the existence of ordered phases of encapsulated diamondoids into carbon nanotubes

We have investigated some diamondoids encapsulation into single walled carbon nanotubes (with diameters ranging from1.0 up to 2.2 nm) using fully atomistic molecular dynamics simulations. Diamondoids are the smallest hydrogen-terminated nanosized diamond-like molecules. Diamondois have been investigated for a large class of applications, ranging from oil industry to pharmaceuticals. Molecular ordered phases were observed for the encapsulation of adamantane, diamantane, and dihydroxy diamantanes. Chiral ordered phases, such as; double, triple, 4- and 5-stranded helices were also observed for those diamondoids. Our results also indicate that the modification of diamondoids through chemical functionalization with hydroxyl groups can lead to an enhancement of the molecular packing inside the carbon nanotubes in comparison to non-functionalized molecules. For larger diamondoids (such as, adamantane tetramers), we have not observed long-range ordering, but only a tendency of incomplete helical structural formation. © 2012 Materials Research Society.

Molecular and morphological data support the existence of a sexual cycle in species of the genus Paracoccidioides

The genus Paracoccidioides includes the thermodimorphic species Paracoccidioides brasiliensis and P. lutzii, both of which are etiologic agents of paracoccidioidomycosis, a systemic mycosis that affects humans in Latin America. Despite the common occurrence of a sexual stage among closely related fungi, this has not been observed with Paracoccidioides species, which have thus been considered asexual. Molecular evolutionary studies revealed recombination events within isolated populations of the genus Paracoccidioides, suggesting the possible existence of a sexual cycle. Comparative genomic analysis of all dimorphic fungi and Saccharomyces cerevisiae demonstrated the presence of conserved genes involved in sexual reproduction, including those encoding mating regulators such as MAT, pheromone receptors, pheromone-processing enzymes, and mating signaling regulators. The expression of sex-related genes in the yeast and mycelial phases of both Paracoccidioides species was also detected by realtime PCR, with nearly all of these genes being expressed preferentially in the filamentous form of the pathogens. In addition, the expression of sex-related genes was responsive to the putative presence of pheromone in the supernatants obtained from previous cocultures of strains of two different mating types. In vitro crossing of isolates of different mating types, discriminated by phylogenetic analysis of the α-box (MAT1-1) and the high-mobility-group (HMG) domain (MAT1-2), led to the identification of the formation of young ascocarps with constricted coiled hyphae related to the initial stage of mating. These genomic and morphological analyses strongly support the existence of a sexual cycle in species of the genus Paracoccidioides. © 2013, American Society for Microbiology.

Multilocus molecular phylogeny of Gasteropelecidae (Ostariophysi: Characiformes) reveals the existence of an unsuspected diversity

The characiform family Gasteropelecidae, the so-called freshwater hatchetfishes, is comprised of three genera and nine species found in Panama and all South American countries except Chile. Our goal was to investigate the molecular characteristics, phylogenetic relationships among the species and genera of Gasteropelecidae and phylogenetic relationships between the Gasteropelecidae family with other Characiformes. DNA fragments from two mitochondrial (16S rRNA and Cytochrome B) and three nuclear genes (Rag1, Rag2 and Myh6) were sequenced. Our results corroborate the morphology-based hypothesized monophyly of the Gasteropelecidae family and most of the relationships among its genera. However, the genus Gasteropelecus is polyphyletic because G. maculatus is placed as the sister group to all other gasteropelecids, whereas G. sternicla is more closely related to species of Carnegiella. Similarly, the species Carnegiella strigata is not monophyletic, which suggests that the family needs a taxonomic review. Moreover, the species Thoracocharax stellatus was composed by four distinct lineages suggesting the this species may represents a species complex. © 2013 Elsevier Inc.

Multiplicity of solutions for a biharmonic equation with subcritical or critical growth

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)