Isotopic liftings of Clifford algebras and applications in elementary particle mass matrices

Isotopic liftings of algebraic structures are investigated in the context of Clifford algebras, where it is defined a new product involving an arbitrary, but fixed, element of the Clifford algebra. This element acts as the unit with respect to the introduced product, and is called isounit. We construct isotopies in both associative and non-associative arbitrary algebras, and examples of these constructions are exhibited using Clifford algebras, which although associative, can generate the octonionic, non-associative, algebra. The whole formalism is developed in a Clifford algebraic arena, giving also the necessary pre-requisites to introduce isotopies of the exterior algebra. The flavor hadronic symmetry of the six u,d,s,c,b,t quarks is shown to be exact, when the generators of the isotopic Lie algebra su(6) are constructed, and the unit of the isotopic Clifford algebra is shown to be a function of the six quark masses. The limits constraining the parameters, that are entries of the representation of the isounit in the isotopic group SU(6), are based on the most recent limits imposed on quark masses.Comment: 19 page

Modelling and control of a high redundancy actuator

The high redundancy actuation concept is a completely new approach to fault tolerance, and it is important to appreciate that it provides a transformation of the characteristics of actuators so that the actuation performance (capability) degrades slowly rather than suddenly failing, even though individual elements themselves fail. This paper aims to demonstrate the viability of the concept by showing that a highly redundant actuator, comprising a relatively large number of actuation elements, can be controlled in such a way that faults in individual elements are inherently accommodated, although some degradation in overall performance will inevitably be found. The paper introduces the notion of fault-tolerant systems and the highly redundant actuator concept. Then a model for a two by two configuration with electro-mechanical actuation elements is derived. Two classical control approaches are then considered based on frequency domain techniques. Finally simulation results under a number of faults show the viability of the approach for fault accommodation without re-configuratio

Phosphorus nutrition and management – overcoming constraints to wider adoption

The importance of phosphorus nutrition for cattle grazing northern Australian rangelands has been well documented and demonstrated. Phosphorus is clearly one of the most important nutritional deficiencies, within the limitations of potential metabolizable energy intakes, of grazing cattle in the seasonally dry tropics. Nevertheless it appears that only a small proportion of cattle grazing phosphorus deficient pastures are supplemented or otherwise managed to alleviate phosphorus deficiency. Estimated requirements for dietary phosphorus by various classes of cattle grazing tropical pastures have recently been revised (CSIRO 2007). The development of faecal near infrared spectroscopy (F.NIRS) allows the routine estimation of metabolizable energy and nitrogen concentrations in the diet, and thus the potential productivity, of cattle grazing northern rangelands. The concentration of phosphorus in the diet of grazing cattle can be estimated from the concentration of phosphorus in the faeces, at least in cattle not fed phosphorus supplements. Combining estimates of diet metabolizable energy, nitrogen and phosphorus allows estimation whether current needs of the animal are supplied by the diet. Phosphorus-replete cattle have substantial body reserves of phosphorus which can be mobilized, especially in late pregnancy and lactation, to alleviate a dietary deficiency. However, these body reserves need to be replenished in late lactation or post-lactation if mobilization occurs each year. Diagnosis of subclinical phosphorus deficiency in grazing cattle, and prediction of animal responses to phosphorus supplements is difficult. In growing cattle the concentration of inorganic phosphorus in blood (Pi), in the late wet or early dry season, combined with information on diet metabolizable energy and nitrogen concentrations obtained by F.NIRS, provides the most reliable test. In pregnant or lactating cows measurements of faecal phosphorus concentration and F.NIRS provide the best estimate of whether phosphorus intake meets the current needs of the animal. However, estimates of adequacy of phosphorus supply need to also consider possible mobilization of body phosphorus reserves. Indicative responses to provision of phosphorus supplements by cattle grazing pastures ranging from marginal to acute deficiency are summarized. Economic evaluation of benchmark enterprises where cattle are expected to be phosphorus deficient indicate that phosphorus supplementation is highly cost-effective. Major obstacles to more widespread adoption of phosphorus supplementation appear to be lack of knowledge and appreciation by managers of the phosphorus status of their cattle, lack of appreciation of the cost-effectiveness of a phosphorus supplementation particularly for some classes of cattle, and the practical difficulties in implementing phosphorus supplementation during the wet season

The economics of phosphorus supplementation of beef cattle grazing northern Australian rangelands

Context: Phosphorus (P) deficiency occurs in beef cattle grazing many rangeland regions with low-P soils, including in northern Australia, and may severely reduce cattle productivity in terms of growth, reproductive efficiency and mortality. However, adoption of effective P supplementation by cattle producers in northern Australia is low. This is likely to be due to lack of information and understanding of the profitability of P supplementation where cattle are P-deficient. Aims: The profitability of P supplementation was evaluated for two dissimilar regions of northern Australia, namely (1) the Katherine region of the Northern Territory, and (2) the Fitzroy Natural Resource Management (NRM) region of central Queensland. Methods: Property-level, regionally relevant herd models were used to determine whole-of-business productivity and profitability over 30 years. The estimated costs and benefits of P supplementation were obtained from collation of experimental data and expert opinion of persons with extensive experience of the industry. The economic consequences of P supplementation at the property level were assessed by comparison of base production without P supplementation with the expected production of P-supplemented herds, and included the implementation phase and changes over time in herd structure. In the Katherine region, it was assumed that the entire cattle herd (breeders and growing cattle) grazed acutely P-deficient land types and the consequences of (1) no P supplementation, or P supplementation during (2) the dry season, or (3) both the wet and dry seasons (i.e. 3 scenarios) were evaluated. In the Fitzroy NRM region, it was assumed that only the breeders grazed P-deficient land types with three categories of P deficiency (marginal, deficient and acutely deficient), each with either (1) no P supplementation, or P supplementation during (2) the wet season, (3) the dry season, or (4) both the wet and dry seasons (i.e. 12 scenarios). Key results: In the Katherine region, year-round P supplementation of the entire cattle herd (7400 adult equivalents) grazing acutely P-deficient pasture resulted in a large increase in annual business profit (+AU$500 000). Supplementing with P (and N) only in the dry season increased annual business profit by +AU$200 000. In the Fitzroy NRM region, P supplementation during any season of the breeder herd grazing deficient or acutely P-deficient pastures increased profit by +AU$2400–AU$45 000/annum (total cattle herd 1500 adult equivalents). Importantly, P supplementation during the wet season-only resulted in the greatest increases in profit within each category of P deficiency, comprising +AU$5600, AU$6300 and AU$45 000 additional profit per annum for marginal, deficient and acutely P-deficient herds respectively. Conclusions: The large economic benefits of P supplementation for northern beef enterprises estimated in the present study substantiate the current industry recommendation that effective P supplementation is highly profitable when cattle are grazing P-deficient land types. Implications: The contradiction of large economic benefits of P supplementation and the generally low adoption rates by the cattle industry in northern Australia suggests a need for targeted research and extension to identify the specific constraints to adoption, including potential high initial capital costs

Coulomb Phase Gluon Scattering at Strong Coupling

We calculate corrections to gluon scattering amplitudes in a Coulomb phase using gauge/string duality. The Coulomb phase considered is a maximal rank breaking of $SU(n_1+n_2)\to SU(n_1)\times SU(n_2) \times U(1)$. This problem therefore has 3 scales involved: 1) the scale of the massive fields $M_W$ arising from the spontaneous breaking of the gauge group; 2) The scale of the scattering, characterized by the Mandelstam variables $s,t,u$; 3) The IR regulator $m_{IR}$. We find corrections in the hard scattering limit $|s|,|t|,|u|\gg m_{IR}^2 \gg M_W^2$, and also find below threshold corrections with $M_W^2 \gg |s|,|t|,|u|$. We find that the corrections in the second case are finite, and so are IR regulator independent.Comment: 17+17 pages, 3 figure

Stringy Probe Particle and Force Balance

We directly derive the classical equation of motion, which governs the centre of mass of a test string, from the string action. In a certain case, the equation is basically same as one derived by Papapetrou, Dixon and Wald for a test extended body. We also discuss the force balance using a stringy probe particle for an exact spinning multi-soliton solution of Einstein-Maxwell-Dilaton-Axion theory. It is well known that the force balance condition yields the saturation of the Bogomol'nyi type bound in the lowest order. In the present formulation the gyromagnetic ratio of the stringy probe particle is automatically determined to be $g=2$ which is the same value as the background soliton. As a result we can confirm the force balance via the gravitational spin-spin interaction.Comment: 8 pages, references added, comments added, Phys. Rev. D accepte

On the Bohr inequality

The Bohr inequality, first introduced by Harald Bohr in 1914, deals with finding the largest radius $r$, $0<r<1$, such that $\sum_{n=0}^\infty |a_n|r^n \leq 1$ holds whenever $|\sum_{n=0}^\infty a_nz^n|\leq 1$ in the unit disk $\mathbb{D}$ of the complex plane. The exact value of this largest radius, known as the \emph{Bohr radius}, has been established to be $1/3.$ This paper surveys recent advances and generalizations on the Bohr inequality. It discusses the Bohr radius for certain power series in $\mathbb{D},$ as well as for analytic functions from $\mathbb{D}$ into particular domains. These domains include the punctured unit disk, the exterior of the closed unit disk, and concave wedge-domains. The analogous Bohr radius is also studied for harmonic and starlike logharmonic mappings in $\mathbb{D}.$ The Bohr phenomenon which is described in terms of the Euclidean distance is further investigated using the spherical chordal metric and the hyperbolic metric. The exposition concludes with a discussion on the $n$-dimensional Bohr radius

Complete Order alpha_s^3 Results for e^+ e^- to (gamma,Z) to Four Jets

We present the next-to-leading order (O(alpha_s^3)) perturbative QCD predictions for e^+e^- annihilation into four jets. A previous calculation omitted the O(alpha_s^3) terms suppressed by one or more powers of 1/N_c^2, where N_c is the number of colors, and the `light-by-glue scattering' contributions. We find that all such terms are uniformly small, constituting less than 10% of the correction. For the Durham clustering algorithm, the leading and next-to-leading logarithms in the limit of small jet resolution parameter y_{cut} can be resummed. We match the resummed results to our fixed-order calculation in order to improve the small y_{cut} prediction.Comment: Latex2e, 17 pages with 5 encapsulated figures. Note added regarding subsequent related work. To appear in Phys. Rev.

Structural Analysis of Narratives with the Coq Proof Assistant

Abstract. This paper proposes a novel application of Interactive Proof Assistants for studying the formal properties of Narratives, building on recent work demonstrating the suitability of Intuitionistic Linear Logic as a conceptual model. More specifically, we describe a method for modelling narrative resources and actions, together with constraints on the story endings in the form of an ILL sequent. We describe how well-formed narratives can be interpreted from cut-free proof trees of the sequent obtained using Coq. We finally describe how to reason about narratives at the structural level using Coq: by allowing to prove 2nd order properties on the set of all the proofs generated by a sequent, Coq assists the verification of structural narrative properties traversing all possible variants of a given plot

Laser printing of silver-based micro-wires in ZrO2 substrate for smart implant applications

Smart implants are endowed with functions of sensing, actuating and control to solve problems that may arise during their use. The assembly of these functions along the implant surface is still a challenge. However, with the advent of 3D printing, it is possible to print on implants’ surface, communication channels or micro-antennas or even sensoric/actuating areas. Hence, a positive impact on the long-term performance of the implants (including hip, dental and knee) may be expected with the proposed approach. Despite titanium and Ti6Al4V titanium alloy are the standard choice for implants fabrication, 3Y-TZP (tetragonal 3% mol yttria-stabilized zirconia) has emerged as a ceramic material suitable to overcome titanium alloy problems, due to its numerous advantages. In this sense, this work is concerned with the ability of printing silver-based communication system in zirconia substrates by using laser technology. For this purpose, micro-cavities were created on ZrO2 substrate, where the silver powder was placed and sintered into them. Through the laser approach, silver-based wires with great quality and low resistivity values were achieved. The flexural strength results showed that the mechanical resistance of zirconia disks was affected by laser micro-wire printing, which decreased as the laser passage was performed. Based on the results, it is believed that the proposed approach seems to be effective for the manufacturing of implants with intrinsic capacities, useful for smart implant applications.This work has been supported by FCT (Fundação para a Ciência e Tecnologia - Portugal) in the scope of the projects UID/EEA/04436/ 2019 and NORTE-01-0145-FEDER-000018-HAMaBICo and Add.Additive_Manufacturing to Portuguese Industry_POCI-01-0247- FEDER-024533. Thank the CNPq (205791/2014-0) and CAPES for the financial support