Standard model and gravity from spinors

It is shown how the Lorentz and standard-model gauge groups can be unified by using algebraic spinors of the standard four-dimensional Clifford algebra, in left–right symmetric fashion. This defines a framework of unification with gravity and generates exactly a standard-model family of fermions, while a Pati–Salam unification group emerges, at the Planck scale, where (chiral) gravity decouples. We show that this low-energy broken phase emerges from the VEV of extended vierbein fields, which at this stage are assumed to be dynamically generated from a theory in the fully symmetric phase valid beyond the Planck scale (and whose consistency and dynamics is thus yet to be assessed) providing thus a geometrical and group-theoretical framework for the unification and breaking. At low energy, on the other hand, it is intriguing to find, as a remnant of this unification, new isospin-triplet spin-two particles that may naturally lie at the weak scale, providing a striking signal at the LHC.     

Fisher zeros in the Kallen–Lehmann approach to 3D Ising model

The distribution of the Fisher zeros in the Kallen–Lehmann approach to three-dimensional Ising model is studied. It is argued that the presence of a non-trivial angle (a cusp) in the distribution of zeros in the complex temperatures plane near the physical singularity is realized through a strong breaking of the 2D Ising self-duality. Remarkably, the realization of the cusp in the Fisher distribution ultimately leads to an improvement of the results of the Kallen–Lehmann ansatz. In fact, excellent agreement with Monte Carlo predictions both at high and at low temperatures is observed. Besides, agreement between both approaches is found for the predictions of the critical exponent α   and of the universal amplitude ratio Δ=A₊/A₋$\Delta =A_{+}/A_{-}$, within the 3.5% and 7% of the Monte Carlo predictions, respectively.     

Simple condensation of composite bosons in a number conserving approach to many fermion-systems

We recently proposed an exact bosonization procedure which generates a Hamiltonian of composite bosons interacting among themselves and with fermionic quasiparticles. The interaction among composites whose mixing is allowed by symmetries is strong, but a simple condensate cannot have a significant mixing with other composites. We determine the conditions of decoupling, study their effects and compare the results with the Random Phase Approximation and the BCS theory.     

Batch Experiments for the Determination of the Ti(IV,III) Couple Formal Potential in 1 mol⋅dm<Superscript>−3</Superscript> HCl, 2 mol⋅dm<Superscript>−3</Superscript> NaCl Medium at 25 °C

The determination of the Ti(IV,III) redox couple formal potential in 1 mol⋅dm⁻³ HCl, 2 mol⋅dm⁻³ NaCl medium at 25 °C through batch experiments involving the preparation of Ti(IV) and Ti(III) mixtures via the reaction of Ti(IV) with zinc amalgam, has been carried out with Emf measurements in order to verify the correctness of the previous value that the authors obtained by a coulometric-potentiometric investigation in the same conditions. The results from the two independent methods are in good agreement: (9±1) mV by the first method and (9±2) mV by the average batch result.     

Calculations of overtone NIR and NIR-VCD spectra in the local mode approximation: Camphor and Camphorquinone

We present a method to calculate near-infrared (NIR) and NIR-vibrational circular dichroism (NIR-VCD) spectra up to the second CH-stretching overtone region in the local mode approximation. Atomic polar tensors and atomic axial tensors are first evaluated by DFT methodology for all CH stretching coordinates with systematic positive and negative displacements off-equilibrium and therefrom anharmonic dipole moment functions are constructed by polynomial interpolations. No adjustable parameters are employed up to this point. Rotational and dipole strengths are finally calculated by evaluating transition moments of Morse-type wave-functions. The method is applied to the case of Camphor and Camphorquinone, for which relevant differences in the vibrational circular dichroism (VCD) data are observed, which are predicted by our approach. Further steps are still to be made for a more complete treatment: the ab initio evaluation of mechanical anharmonicity and the introduction of mechanical and electrical coupling between local modes.     

In vivo absorption spectra of the two stable states of the Euglena photoreceptor photocycle

Euglena gracilis possesses a simple but sophisticated light detecting system, consisting of an eyespot formed by carotenoids globules and a photoreceptor. The photoreceptor of Euglena is characterized by optical bistability, with two stable states. In order to provide important and discriminating information on the series of structural changes that Euglena photoreceptive protein(s) undergoes inside the photoreceptor in response to light, we measured the in vivo absorption spectra of the two stable states A and B of photoreceptor photocycle. Data were collected using two different devices, i.e. a microspectrophotometer and a digital microscope. Our results show that the photocycle and the absorption spectra of the photoreceptor possess strong spectroscopic similarities with a rhodopsin-like protein. Moreover, the analysis of the absorption spectra of the two stable states of the photoreceptor and the absorption spectrum of the eyespot suggests an intriguing hypothesis for the orientation of microalgae toward light.     

Extension results for slice regular functions of a quaternionic variable

In this paper we prove a new Representation Formula for slice regular functions, which shows that the value of a slice regular function f at a point q=x+yI can be recovered by the values of f at the points q+yJ and q+yK for any choice of imaginary units I,J,K. This result allows us to extend the known properties of slice regular functions defined on balls centered on the real axis to a much larger class of domains, called axially symmetric domains. We show, in particular, that axially symmetric domains play, for slice regular functions, the role played by domains of holomorphy for holomorphic functions.     

A gap property for the growth of closed 3-manifold groups

We provide a lower bound for the uniform exponential growth rate of closed nonflat nonpositively curved 3-manifold groups. A detailed study of the uniform exponential growth rate of closed 3-manifold groups is also presented.     

Shuffles of copulas

We show that every copula that is a shuffle of Min is a special push-forward of the doubly stochastic measure induced by the copula M. This fact allows to generalize the notion of shuffle by replacing the measure induced by M with an arbitrary doubly stochastic measure, and, hence, the copula M by any copula C.     

Interval conjectures for level Hilbert functions

We conjecture that the set of all Hilbert functions of (artinian) level algebras enjoys a very natural form of regularity, which we call the Interval Conjecture (IC): If, for some positive integer α, $(1,h_1,\dots ,h_i,\dots ,h_e)$ and $(1,h_1,\dots ,h_i+\alpha ,\dots ,h_e)$ are both level h-vectors, then $(1,h_1,\dots ,h_i+\beta ,\dots ,h_e)$ is also level for each integer $\beta =0,1,\dots ,\alpha$. In the Gorenstein case, i.e. when $h_e=1$, we also supply the Gorenstein Interval Conjecture (GIC), which naturally generalizes the IC, and basically states that the same property simultaneously holds for any two symmetric entries, say $h_i$ and $h_{e?i}$, of a Gorenstein h-vector.These conjectures are inspired by the research performed in this area over the last few years. A series of recent results seems to indicate that it will be nearly impossible to characterize explicitly the sets of all Gorenstein or of all level Hilbert functions. Therefore, our conjectures would at least provide the existence of a very strong — and natural — form of order in the structure of such important and complicated sets.We are still far from proving the conjectures at this point. However, we will already solve a few interesting cases, especially when it comes to the IC, in this paper. Among them, that of Gorenstein h-vectors of socle degree 4, that of level h-vectors of socle degree 2, and that of non-unimodal level h-vectors of socle degree 3 and any given codimension.