Ternary Forms Research Articles

Tuning the reactivity of tri-s-triazine, trinitro-tri-s-triazine and ternary tri-s-triazine graphitic C3N4 quantum dots through H-functionalized and B-doped complexes: A density functional study

Modifying the structures and doping are proven to be effective methods to tune the structural and electrical properties of g-C3N4 quantum dots. Hence, in this study, tri-s-triazine and tri-nitro tri-s-triazine have been studied by functionalizing their edges with hydrogen. The H-functionalized tri-nitro tri-s-triazine quantum dot displays a buckled structure with a band gap of 1.988 eV, whereas the tri-s-triazine demonstrates a planner structure with a band gap of 1.636 eV. The obtained results have been compared with the previous results. The absorbance spectrum of H-functionalized trinitro tri-s-triazine falls under the visible region with a peak value of 488 nm, and the absorption spectrum of tri-s-triazine falls at 790 nm. The planarity of the tri-nitro tri-s-triazine structure is improved by doping the B atom in the N site, and the band gap of H-functionalized B doped tri-nitro tri-s-triazine is 1.143 eV. The absorbance spectrum of H-functionalized B doped tri-nitro tri-s-triazine is 508 nm. The reactivity of the structure is increased by doping B atoms, and it is confirmed by the electrophilicity index. Similarly, the H-functionalized B doped tri-s-triazine exhibits a band gap of 1.328 eV. Further, the tri-s-triazine structures are arranged in ternary form, and the properties are studied by increasing the number of B atoms in the tri-s-triazine rings. The outcome presents that the structures are planar, and band gap values are reduced further. Also, the reactivity of the sheets is increased, which is confirmed by the electrophilicity index. It is proposed that the sheets with a high reactivity can be used for the removal of hazardous ions and molecules from the industrial wastage.

Phase Equilibria in the Al-Cr-Co System in the Range of Compositions 0-70 at.% Al

Phase equilibria during solidification in the Al-Cr-Co system in the range of compositions 0-70 at.% Al were studied using optical microscopy, scanning electron microscopy, electron probe microanalysis, differential thermal analysis and x-ray diffraction. Solidus and liquidus surfaces, a melting diagram as their superposition, a Scheil diagram for solidification, as well as series of isopleths were constructed for the first time. Solid solutions based on Cr, αCo, Cr5Al8 (γ3 and γ1 phases), CoAl, Co2Al5 binary compounds and the ternary compound τ5 take part in phase equilibria. The monoclinic ternary compound τ5 forms by peritectic reaction L + γ1 + Co2Al5 ↔ τ5 at 1065 °C. Four invariant four–phase reactions and one invariant three–phase reaction involving liquid take place at 1280, 1175, 1110, 1065 and about 1480 °C, respectively. Isopleths 10, 20, 30 and 40 at.% Al as well as 40 at.% Cr demonstrate peculiarities of the phase diagram.

Effect of TiO2, Al2O3 and CaCO3 nano-additives in singular, binary and ternary forms on the mechanical, thermal and microstructural propertites of fly ash supplemented cement matrix

In this paper, we focus on how nanoadditives such as nano-Al2O3, nano-TiO2 and nano-CaCO3 modify the mechanical and capillary permeability of fly ash cement mortars (5:1). When nanoadditives are added in proportions of 2%, 4% and 6% of the binder volume, hydration products are generated, and thermal conductivity and microstructure of cement mortars undergo a change. Mechanical property measured at 7, 28 and 90 days are measured to understand the underlying pozzolanic reaction and filling effect. The experimental findings reveal that the form and quantity of refractory chemicals in mortar production had an impact hardened matrix at the early age between 7 and 28 days, but thereafter, there is only a marginal strength gain. Nano-Al2O3 and nano-CaCO3 (at 2% of binder volume) additives were able to increase the mortar strength to the extent of 27% of the 28-day compressive strength at 7 days. The addition of 2% nano-TiO2 did not produce this effect. The addition of 6% nano-Al2O3 + nano-CaCO3 in binary and 6% nano-TiO2 + nano-Al2O3 + nano-CaCO3 blend in ternary combinations produced a phenomenally positive effect on the compressive strength with the reduction of capillary permeability at 90 days of setting. The X-ray diffraction patterns of these matrices compared with control showed a clear evidence of reduction of CH growth. Formation of a compact binding gel can be observed in scanning electron microscopic (SEM) pictures. A dense microstructure of binary and ternary nano additive mixes is establish to be favourable in decreasing the thermal conductivity of fly ash blend cement mortar measured at 30 °C. The combination of non-siliceous nano-size materials such as nano-Al2O3, nano-TiO2 and nano-CaCO3 in small quantities have an impact on the pozzolanic reaction with continual strength gain and are effective in counteracting the shortcomings of fly ash blended with cement mortars.

Water remediation using biosorbent obtained from agricultural and fruit waste

In rural community, groundwater is the main source of drinking water. Due to negative health impacts of excess fluoride in drinking water, there is urgent need to search the low-cost techniques to remove fluoride. Several materials have been used as adsorbent for removal of fluoride. Different parts of plant such as bark, stem, root, and leaves have cellulose, hemicelluloses, lignin etc. that are generally discarded as agricultural waste. Similarly, after using pulp of fruits, seeds and peels of fruits are considered as waste and cause environmental pollution when dumped at open places or near water bodies. These waste materials can be efficiently used for removal of fluoride from water. Biosorption is an eco-friendly process in which ions bind to biomass and can be extracted from the solution. Biosorption by means of adsorbent powder obtained from agricultural waste in the form of Sugarcane bagasse powder (SBP), Rice husk ash (RHA), Waste fruit peel powder (WFPP) and Powder blend (PB) have been used in this study for removal of fluoride ions. These biological materials have been explored in single, binary and ternary forms and have been found most usable as PB form in acidic medium with 85% removal of fluoride. This process has been signified as an eco-friendly, cost-effective approach for the isolation of fluoride ions from aquatic environments.

Reproductive toxicity in male juvenile rats: Antagonistic effects between isolated agrochemicals and in binary or ternary combinations

The management of agrochemicals in Brazilian agriculture impacts global environmental sustainability and food security, since this country is one of the major agro-food exporters in the world. Acephate, carbendazim, and dithiocarbamates (DTCs) such as mancozeb, are among the most detected agrochemicals in Brazilian agro-food products, occurring in combination in several crops, especially in fruit cultures. The present study evaluated the impact of the exposure to isolated agrochemicals and all the combined possible mixtures (binary and ternary forms) on the reproductive parameters of male juvenile rats, known to be a vulnerable biological system and developmental window. Data were analyzed using Generalized Linear Models (GzLM), considering each agrochemical as an independent factor. The study revealed higher reproductive toxicity exerted by isolated agrochemicals when compared to the combined treatments, which exhibited mostly an antagonistic effect. Results suggest endocrine disruptive effects of each one separately on the weight of reproductive organs and testicular histomorphometry, besides changes in testicular SOD activity. The full factorial experimental design employed here allowed us to conclude that it is not possible to scale-up the effects of the isolated treatments to the mixtures, showing how difficult it is to know beforehand the response and cross-talk among the multiple physiological mechanisms disturbed by complex mixtures. Considering that food products are shared on a global scale and that some of these three agrochemicals have already been prohibited in EU countries, the consumption of some Brazilian products puts global human health at risk, that of children.

Inverse Numerical Range and Determinantal Quartic Curves

A hyperbolic ternary form, according to the Helton–Vinnikov theorem, admits a determinantal representation of a linear symmetric matrix pencil. A kernel vector function of the linear symmetric matrix pencil is a solution to the inverse numerical range problem of a matrix. We show that the kernel vector function associated to an irreducible hyperbolic elliptic curve is related to the elliptic group structure of the theta functions used in the Helton–Vinnikov theorem.

ANN Based Prediction of Engine Performance and Exhaust Emission Responses of a CI Engine Powered By Ternary Blends

In this study, experimental data was gathered from a single cylinder diesel engine fuelled with pyrolytic oil, neat diesel and butanol fuel blends. The experiments were conducted at varying engine loads from 0.25 kW to 1 kW with the interval of 0.25 kW. The engine performance and emission data obtained were predicted using an artificial neural network (ANN) algorithm. Assessed responses are CO, NOx, BSFC, and BTE. The results were discussed in terms of R2, MBE, and RMSE metrics. The performance and emission responses were predicted with a good R2 value of 0.986, 0.963, 0.991, and 0967 for BTE, BSFC, NOx, and CO, respectively, and all MBE value is very close to zero and smaller than 1.14. In the conclusion, the present paper showed that the ternary form of n-butanol-pyrolytic fuel and diesel fuel can be used in a CI engine with no modification on the vehicular system and the emission and performance responses of ternary fuels can be accurately predicted using an artificial neural network.

The Potential of Recycled Aggregates and Coconut Fiber in the Production of Concrete

The high cost of conventional construction materials has led researchers into the search for alternative construction materials that are sustainable and eco-friendly. This study investigates the effect of crushed sandscrete block as recycled fine aggregate (RFA) and crushed abandoned cubes as recycled coarse aggregate (RCA) with constant percentage of coconut fibre (CF) on the properties of the concrete. The normal aggregate concrete (NAC) containing normal aggregate (NA) without the addition of CF was first produced and tested. The second stage involved production of concrete comprising constant percentage of CF with 25%, 50%, 75% and 100% fine and coarse aggregate replacement by weight with RFA and RCA. Properties of fresh and hardened concrete for all specimen types with standard procedure to obtain an optimum mix design was determined. The results obtained from the study shows that the workability of all the replacements were found to be lower than that of the normal aggregate concrete (NAC). Compressive and splitting tensile strength test showed that at optimum replacement levels of 25% RCA and 25% RFA concrete have better strength performance than NAC. The study established that RCA and RFA is capable of partially replacing NA in concrete production in ternary form. The optimum percentage replacement of RCA, RFA and CF should be adhered to for effective performance.

Perception of the ternary arch-form in Western concert music: evidence from college music education

ABSTRACT This study focuses on listeners’ form perception as they encounter Western concert music. The general aim was to investigate college music students’ form perception as they listen to five long-range concert works of different styles, all analyzed by the author as having an overall ternary ABA’ arch-form. Five groups of college music students (N=126) listened respectively to five ternary arch-form compositions by Chopin, Mussorgsky, Tchaikovsky, Bartók and Schönberg. Each group was required to identify the musical form of one test-piece and convey responses both through written notes and self-invented notations. Significant differences were found between the five test-pieces in the percentage of participants who confirmed the ternary form analysis and participants who interpreted the form as binary. Also, significant differences were found in (i) five cue-parameters contributing to form detection: tempo, timbre, pitch, articulation and mood; (ii) in emotional and metaphoric responses evoked by the music; and (iii) in the use of colour in visual representations of musical form. A significant association between auditory/ternary perception and graphic/ternary designs was found in works by Chopin, Mussorgsky and Bartók. Results bear implications for the teaching and learning of structural listening in Western concert music.

Reprise Structures in Haydn’s Op. 50 Minuets

Reprise Structures in Haydn’s Op. 50 Minuets Samantha M. Inman (bio) Over-enthusiasm for the epic too easily directs admiration away from the skills needed to create a miniature masterpiece.1 A minuet, with respect to execution, is no different from a concerto, an aria, or a symphony,” Joseph Riepel asserts.2 Indeed, the first two chapters of his Anfangsgründe zur musicalischen Setzkunst demonstrate how aspects of phrase structure and motivic development apply to genres ranging from the humble to the prestigious. This approach to composition pedagogy highlights the need for basic skills that can be honed in small-scale works and applied to large-scale works. Conversely, creative manipulations typically associated with large forms may be used to enliven small forms. This principle is evident in the minuets by Joseph Haydn. Early biographer G. A. Griesinger hints at the value the composer placed on the minuet in the following anecdote: “Someone told Haydn that Albrechtsberger wished to see all fourths banished from the purest style. ‘What does that mean?’ replied Haydn…. ‘Such affectations [End Page 23] are worthless. I would rather someone tried to compose a really new minuet.’”3 Haydn’s own minuets encompass sophisticated compositional techniques, attesting to his own search for new ways of writing in familiar genres. Past studies of Haydn’s minuets in string quartets or symphonies have employed analytic tools such as hypermeter and topic theory.4 However, even fundamental aspects of tonality and form in these dances can reward close examination. This case study considers Haydn’s Op. 50 string quartets for four reasons. First, extant literature acknowledges the complexity of Haydn’s quartet movements in general and the quartet minuet movements in particular.5 Second, focusing on a single opus highlights the variety in pieces composed within a short time span. Written for Friedrich [End Page 24] Wilhelm II from Prussia, all six of these quartets were completed and published in 1787.6 Third, outside of W. Dean Sutcliffe’s excellent monograph on the set, Op. 50 has received less scholarly attention than Haydn’s other groups of string quartets, especially Opp. 20, 33, and 76.7 Fourth, and most importantly, the minuets of Op. 50 provide a particularly fertile field for studying reprise structures. As Sutcliffe notes, “the third movements of Op. 50 … are concerned with matters of dominant preparation and structural return, almost to the point of being a fetish.”8 The present article views the minuet and trio movements from Haydn’s Op. 50 string quartets through the lenses of form and Schenkerian voice leading.9 After a brief overview of the set, analyses of the individual dances are presented in three groups in order of increasing complexity. Just as Haydn’s sonata movements range from textbook to deformational, the minuets in Op. 50 range from conventional to peculiar.10 In fact, the manner in which the minuets depart from expectations reflects features well-documented in his movements in sonata form, including unusual starts to reprises, rewritten recapitulations, and cross-references with material from the digression.11 [End Page 25] Minuets and Trios in Haydn’s Op. 50: An Overview All six minuet and trio movements in Haydn’s Op. 50 follow the conventional compound ternary form encompassing two binary forms. Furthermore, each nested binary form is at least arguably rounded, featuring a reprise.12 The harmonic ending to the first part of a binary form determines the extent to which modifications must be made in a reprise. As Table 1 shows, Op. 50 contains representatives of two different types: sectional and continuous. Sectional forms, which close their first section with an authentic cadence in the tonic key, require no alteration; repetition of the entire passage at the end of the second section yields satisfactory closure. In contrast, continuous forms require modification in order to reach tonal closure, altering a half cadence to an authentic cadence or rewriting a modulating first section to conclude in tonic. Despite the different tendencies of sectional and continuous forms, Haydn’s Op. 50 contains instances of minimal and radical alterations in both categories, as Table 1 indicates.13 While five out of the [End Page 26] Click for larger view...

Analytical and Experimental study on load-deflection characteristics of Ternary blend SCC beams

Development of newer concrete is the need of the hour to meet out today’s demand due to fast growing construction activities. Taller constructions with lesser space involve closer reinforcements lead to suffer the reach of concrete uniformly. Hence concrete with higher degree of flowability without compromising strength comes to the mind of constructor. Such concrete called self-consolidating or compacting concrete and is capable of compacting on its own with no external effort. This paper deals with load deflection performance of such concrete using mineral and chemical admixtures, so that good amount of cement will be minimized without compromising strength and workability. Detailed experimental investigations were done with industrial wastes as replacers to conventional binder (cement) in ternary form. Experimental results of ternary SCC was compared with the results of conventionally vibrated concrete (CVC). Finite element model was developed using ANSYS and was validated with experimental results. It was inferred that ternary SCC beams exhibited more ductile nature compared to CVC beams.

On the identifiability of ternary forms

We describe a new method to determine the minimality and identifiability of a Waring decomposition A of a specific form (symmetric tensor) T in three variables. Our method, which is based on the Hilbert function of A, can distinguish between forms in the span of the Veronese image of A, which in general contains both identifiable and not identifiable points, depending on the choice of coefficients in the decomposition. This makes our method applicable for all values of the length r of the decomposition, from 2 up to the generic rank, a range which was not achievable before. Though the method in principle can handle all cases of specific ternary forms, we introduce and describe it in details for forms of degree 8.

F. Schubert’s last Piano Sonatas in the aspect of his song-like thinking

F. Schubert’s last Piano Sonatas in the aspect of his song-like thinking

Joint differential invariants of binary and ternary forms

We use moving frames to construct and classify the joint invariants and joint differential invariants of binary and ternary forms. In particular, we prove that the differential invariant algebra of ternary forms is generated by a single third order differential invariant. To connect our results with earlier analysis of Kogan, we develop a general method for relating differential invariants associated with different choices of cross-section.

Spectroscopic characterization and photo catalytic degradation ability of ternary oxides of Cobalt

In the present work we have prepared and characterized the two ternary forms of cobalt titanate namely ilmenite and cubic by the sol-gel technique simply by replacing the titanium precursor and using a cationic surfactant micelle solution followed by calcinations at 600°C and 800°C respectively. In both cases, the nanopowders revealed a dark bluish green color, different morphologies of spherical, rhombus and needle shapes with mean particle sizes 29 and 37 nm, respectively. Bearing growing environmental concerns in mind, we have also highlighted a simple nano chemistry based clean and efficient process for effective degradation of hazardous malachite green oxalate dye by an in-situ ultraviolet irradiation set-up. In this field there is hardly any report involving comparative study of ternary oxides of cobalt as potential candidates for photo catalytic degradation. We ultimately observed that cobalt meta titanate proved itself the optimal catalyst at a calcination temperature of 600°C showing a maximum degradation efficiency of 96.38% It also showed a better first-order rate constant of 0.01636 min-1. A decent attempt to correlate photoluminescence and photo catalysis has also been made. Also, a heterojunction has been fabricated with cobalt meta titanate and the parameters of crucial importance in photocatalysis namely conductivity, carrier mobility, transit time evaluated from the current-voltage characteristics.

Optimal density for values of generic polynomial maps

We establish that the optimal bound for the size of the smallest integral solution of the Oppenheim Diophantine approximation problem $|Q(x)-\\xi|<\\epsilon$ for a generic ternary form $Q$ is $|x|\\ll\\epsilon^\{-1\}$. We also establish an optimal rate of density for the values of polynomials maps in a number of other natural problems, including the values of linear forms restricted to suitable quadratic surfaces, and the values of the polynomial map defined by the generators of the ring of conjugation-invariant polynomials on $M_3(\\Bbb\{C\})$. These results are instances of a general approach that we develop, which considers a rational affine algebraic subvariety of Euclidean space, invariant and homogeneous under an action of a semisimple Lie group $G$. Given a polynomial map $F$ defined on the Euclidean space which is invariant under a semisimple subgroup $H$ of the acting group $G$, consider the family of its translates $F\\circ g$ by elements of the group. We study the restriction of these polynomial functions to the integer points on the variety confined to a large Euclidean ball. Our main results establish an explicit rate of density for their values, for generic polynomials in the family. This problem has been extensively studied before when the polynomials in question are linear, in the context of classical Diophantine approximation, but very little was known about it for polynomial of higher degree. We formulate a heuristic pigeonhole lower bound for the density and an explicit upper bound for it, formulate a sufficient condition for the coincidence of the lower and upper bounds, and in a number of natural examples establish that they indeed match. Finally, we also establish a rate of density for values of homogeneous polynomials on homogeneous projective varieties.

PRIME-UNIVERSAL QUADRATIC FORMS AND

A positive-definite diagonal quadratic form $a_{1}x_{1}^{2}+\cdots +a_{n}x_{n}^{2}\;(a_{1},\ldots ,a_{n}\in \mathbb{N})$ is said to be prime-universal if it is not universal and for every prime $p$ there are integers $x_{1},\ldots ,x_{n}$ such that $a_{1}x_{1}^{2}+\cdots +a_{n}x_{n}^{2}=p$. We determine all possible prime-universal ternary quadratic forms $ax^{2}+by^{2}+cz^{2}$ and all possible prime-universal quaternary quadratic forms $ax^{2}+by^{2}+cz^{2}+dw^{2}$. The prime-universal ternary forms are completely determined. The prime-universal quaternary forms are determined subject to the validity of two conjectures. We make no use of a result of Bhargava concerning quadratic forms representing primes which is stated but not proved in the literature.

On a geometric method for the identifiability of forms

We introduce a new criterion which tests if a given decomposition of a given ternary form $T$ of even degree is unique. The criterion is based on the analysis of the Hilbert function of the projective set of points $Z$ associated to the decomposition, and on the Terracini's Lemma which describes tangent spaces to secant varieties. The criterion works in a range for the length of the decomposition which is equivalent to the range in which the reshaped Kruskal's criterion (see [1]) works. Our criterion determines an algorithm for the identifiability of $T$ which is sensibly faster than algorithms based on the reshaped Kruskal's criterion, especially when the set of points $Z$ is not in general position.

Hyperbolic forms admit reversible weighted shift determinantal representation

Lentzos and Pasley recently showed that a weakly circular symmetric invariant hyperbolic ternary form admits a determinantal representation through a cyclic weighted shift matrix. In this paper, we improve the representing matrix by employing a cyclic weighted shift with reversible weights.

Impact of addition of two ether additives with high speed diesel- Calophyllum Inophyllum biodiesel blends on NOx reduction in CI engine

The objective of this work was to compare the effect of diethyl ether (DEE) and methyl tertiary-butyl ether (MTBE) addition to biodiesel and diesel blends on diesel engine. The ethers concentration have been varied in proportion of 5% and 10% on volume basis with biodiesel by keeping the diesel concentration as 50% for all ternary blends preparation. Experimental results revealed that D50-B45-DEE5 ternary blend has shown 5.3% increase in thermal efficiency compared to other ternary blends. On the other hand, D50-B45-MTBE5 and D50-B45-DEE ternary blends have reduced CO emission by 8.1% and 14.8% respectively when compared to high speed diesel fuel. Furthermore, the D50-B40-DEE10 blend and D50-B40-MTBE10 reduce the NOx emission by 32% and 8.8% when compared to HSD at maximum load condition. Significant reduction is noted in HC emission for all ether added ternary blends than that of HSD and biodiesel fuels. However, the smoke emission is decreased marginally for D50-B45-DEE5 than that of HSD fuel. Finally, it is evident that both the DEE and MTBE could be used as viable additive with diesel or biodiesel in binary and ternary forms for diesel engine applications.