Quadratic Forms over Involutorial Division Algebras

We provide an alternative proof of a theorem of Marinacci [2] regarding the equality of two convex-ranged measures. Specifically, we show that, if P and Q are two nonatomic, countably additive probabilities on a measurable space (S,Σ), the condition [∃A∗ ∈ Σ with 0 P (B) =⇒ Q(A) ≥ Q(B)]. Moreover, either one is equivalent to P = Q. JEL Classification Number: D81 In [2], Marinacci proved the following theorem. Theorem (Marinacci [2]) Let P and Q be two finitely additive probabilities on a λ-system Σ. Suppose that P is convex-ranged and thatQ is countably additive. If ∃A∗ ∈ Σ with 0 P (B) =⇒ Q(A) ≥ Q(B). Proposition 1 below shows that this latter is equivalent to P = Q, and Proposition 2 proves the equivalence to Marinacci’s condition. Our condition is probably easier to check in applications. It is in this form, for instance, that the result about the equality of convex-ranged ∗Department of Economics, Columbia University, 1019 IAB, 420 W 118th street, NY, NY 10027. Email: ma734@columbia.edu.

The first key objective of this thesis is to estimate a set of econometric models of Australian broadacre agricultural production by applying the duality theory in production economics. Models of Australian broadacre agriculture are estimated using alternative formulations of econometric modelling of producer decision-making, in which cost minimisation, revenue maximisation and profit maximisation are assumed. A unique, large quasi-micro pooled cross-sectional farm dataset drawn from the Australian Agricultural and Grazing Industries Survey over a sixteen year period, from 1990 to 2005, is used for model estimation. Key policy-relevant outcomes of this investigation are estimates of price elasticities and elasticities of transformation and substitution between broadacre inputs and outputs in Australia. Multi-product dual cost, revenue and profit functions are specified for Australian broadacre agriculture. The multi-product functions are specified to accommodate the prevalent multi-enterprise operation on Australian broadacre farms. The restricted versions of the dual functions are chosen to account for quasi-fixity and the lumpiness of some capital used in broadacre production. The translog and normalised quadratic, the two most popular flexible functional forms in empirical duality applications, are used to specify the dual functions. In addition, impacts of climatic conditions, production focuses, production scales and rainfall on production are also allowed for in the estimated models. Systems of demand and/or supply equations are derived from the specified dual cost, revenue and profit functions and estimated using the quasi-micro dataset available. The estimated systems obtained have reasonable statistical goodness-of-fit with high percentage of statistically significant system coefficients. Price variables are also found to significantly influence input demand and output supply. Importantly, using the normalised quadratic form, the estimated system of input demand derived from the cost function and the estimated system of output supply derived from revenue functions satisfy the theoretical curvature conditions implied by rational economic behaviour. The estimated supply and demand system derived from the profit function violates the curvature condition but the violation is not severe. Input demand and output supply in broadacre farming are found to be fairly inelastic with respect to price changes in the short run. However, demand for fertilisers and crop and pasture chemicals are found to be sensitive to changes in their own prices and in general production costs. The second key objective of this thesis is to investigate three significant issues concerning the application of the duality theory in empirical agricultural production research using data from Australian broadacre agriculture. First, the results obtained from the dual cost, revenue and profit functions are contrasted according to goodness-of-fit, the satisfaction of theoretical regularity conditions and the sensibility of the generated elasticity estimates. The estimation result obtained under the cost minimisation assumption conforms more to economic theory than results obtained under revenue maximisation or profit maximisation. Second, the estimation results are more in line with expectations based on prior economic reasoning when the normalised quadratic functional form is used than when the translog is used. Third, results using data of Australian broadacre farming at two aggregate levels indicate that data aggregation across firms can have a significant impact on research findings, depending on the assumption made regarding the economic behaviour of producers

We derive an adaptive solver for random elliptic boundary value problems, using techniques from adaptive wavelet methods. Substituting wavelets by polynomials of the random parameters leads to a modular solver for the parameter dependence, which combines with any discretization on the spatial domain. We show optimality properties of this solver, and present numerical computations. Introduction Stochastic Galerkin methods have emerged in the past decade as an efficient solution procedure for boundary value problems depending on random data, see [DBO01, XK02, BTZ04, WK05, MK05, FST05, WK06, TS07, BS09, BAS10]. These methods approximate the random solution by a Galerkin projection onto a finite dimensional space of random fields. This requires the solution of a single coupled system of deterministic equations for the coefficients of the Galerkin projection with respect to a predefined set of basis functions on the parameter domain. A major remaining obstacle is the construction of suitable spaces in which to compute approximate solutions. These should be adapted to the stochastic structure of the equation. Simple tensor product constructions are infeasible due to the high dimensionality of the parameter domain in case of input random fields with low regularity. Parallel to but independently from the development of stochastic Galerkin methods, a new class of adaptive methods has emerged, which are set not in the continuous framework of a boundary value problem, but rather on the level of coefficients with respect to a hierarchic Riesz basis, such as a wavelet basis. Due to the norm equivalences constitutive of Riesz bases, errors and residuals in appropriate sequence spaces are equivalent to those in physically meaningful function spaces. This permits adaptive wavelet methods to be applied directly to a large class of equations, provided that a suitable Riesz basis is available. For symmetric elliptic problems, the error of the Galerkin projection onto the span of a set of coefficients can be estimated using a sufficiently accurate approximation of the ∗Research supported in part by the Swiss National Science Foundation grant No. 200021-120290/1.

This paper presents a study of English-Indonesian translation of the humorous utterances in Walt Disney’s Donald Duck comics. Twenty one Indonesian translated comics of the 2008 issues and their original English versions were used as the source of data. A total of 480 humorous English utterances were identified and verified by 4 native English speakers. These 480 English utterances and their translations were used as the data. Analyses of the collected data were then made to see the translation techniques used by the translator in translating the humorous utterances and to see the resulted pragmatic equivalence viewed from the equivalence of pragmatic force between the source text (ST) and target text (TT), involving implicture analysis of the utterances. The findings of the research reveal that 647 uses of translation techniques are made to translate the 480 utterances, as more than one techniques are used in some of the utterances. Seventeen out of 18 translation techniques proposed by Molina & Albir (2002) are chosen by the translator. It is also found out that the translator’s choice of translation techniques has resulted in 96.87% of the translated humorous utterances being equivalent in their pragmatic force, compared to the original English utterances. The use of such translation techniques as generalization, established equivalent, linguistic compression, amplification, literal translation, compensation, linguistic amplification, variation, particularization, borrowing, transposition, description, and calque has resulted in equivalent pragmatic force between ST and TT. Only minor portion (3.13%) of the translated text is not equivalent in its pragmatic force, and this is caused by the use of amplification, discursive creation, reduction, adaptation, and modulation techniques. The high rate of pragmatic equivalence shows the translator’s success in translating the text. Key words : implicature, pragmatic force, pragmatic equivalence, translation technique

In this article, an exact analysis of compressors spool in a turbojet engine has been investigated. The spool is modeled as a rotating thick-walled hollow circular cylinder with free-clamp ends. It is subjected to centrifugal load due to its constant rotational speed, uniform internal and external radial loads and arbitrary thermal gradients. The analysis is initially investigated for the homogeneous state. Then FGM state is investigated to improve the safety factor of the spool. In order to calculate the safety factor, Von-Mises criterion has been used. In FGM state, thermoelastic properties of material would vary in radial direction. The function of these properties changes is assumed exponential. To obtain the highest safety factor, the numerical optimization method has been used and the optimal results have been compared with the homogeneous state. To drive the relations for free-clamp ends boundary condition, at first spool is considered clamp-clamp ends. Then, the effect of releasing one of the ends has been calculated and finally, using the principle of superposition, the results for clamp-free ends state has been investigated. In addition, the effect of changing the non-homogeneous coefficients, spool rotating speed, radial loads and thickness on the safety factor are investigated. Increasing the thickness and radial loads would lead to a change in the optimal coefficient and would result in reducing the safety factor of optimum state. The results showed that utilization of FGM state with optimal coefficient could significantly increase the safety factor and reduce displacements. Furthermore, increasing the rotation speed and radial loads would result in a change in the optimal non-homogeneous coefficient and reduce its equivalent safety factor.

In this paper, we prove a weak form of the conjecture generalised to algebraic number fields. Given integers satisfying , Stewart and Yu were able to give an exponential bound in terms of the radical over the integers (Stewart and Yu [Math. Ann. 291 (1991), 225–230], Stewart and Yu [Duke Math. J. 108 (2001), no. 1, 169–181]), whereas Győry was able to give an exponential bound in the algebraic number field case for the projective height in terms of the radical for algebraic numbers (Győry [Acta Arith. 133 (2008), 281–295]). We generalise Stewart and Yu's method to give an improvement on Győry's bound for algebraic integers over the Hilbert Class Field of the initial number field K. Given algebraic integers in a number field K satisfying , we give an upper bound for the logarithm of the projective height in terms of norms of prime ideals dividing , where L is the Hilbert Class Field of K. In many cases, this allows us to give a bound in terms of the modified radical as given by Masser (Proc. Amer. Math. Soc. 130 (2002), no. 11, 3141–3150). Furthermore, by employing a recent bound of Győry (Publ. Math. Debrecen 94 (2019), 507–526) on the solutions of S‐unit equations, our estimates imply the upper bound where is an effectively computable constant. Further, given conditions on the largest prime ideal dividing , we obtain a sub‐exponential bound for in terms of the radical. Independently, as a direct application of his bounds on the solutions of S‐unit equations(Győry ([Publ. Math. Debrecen 94 (2019), 507–526]), Győry (Publ. Math. Debrecen 100 (2022), 499–511) also attains results mentioned above, including the above inequality, but over the base field K, as discussed in Section 6. As a consequence of our results, we will give an application to the effective Skolem–Mahler–Lech problem and give an improvement to a result by Lagarias and Soundararajan (J. Théor. Nombres Bordeaux 23 (2011), no. 1, 209–234) on the XYZ conjecture.

Let Q denote the rational number field and α be an algebraic number of degree s. Then the algebraic number field F s = Q(α) is the field given by the polynomials in α of degree < s with rational coefficients.

In the present paper we consider initial value problems for Hilfer fractional differential equations and for system of Hilfer fractional differential equations. By using equivalent integral equations and some fixed point theorems, we study the local existence of solutions. We extend these local existence results globally with the help of continuation theorems and generalized Gronwall inequality.

Bernstein’s theorem states that the following properties are equivalent for a function ψ:]0, ∞ [→ R (which then is called completely monotone):moreover, the measure σ in iii) is uniquely determined.

In this thesis, we use integral equation methods to study the scattering of timeharmonic electromagnetic plane waves by biperiodic multilayered structures. Here, such structures are modeled by vertically arranging finitely many non-self-intersecting polyhedral Lipschitz interfaces. We distinguish single profile scatterers and scatterers composed of at least two surfaces. The electromagnetic scattering problem, which arises from the presence of obstacles of the first type, serves as a basic model that we reuse in the multilayered case. By treating it with a combined potential ansatz, we obtain an equivalent new periodic singular integral equation with Fredholm index zero. The Fredholmness is verified by Garding inequalities. This property is crucial for proving one of the main results of our analysis in the single interface setting: an existence theorem for the derived integral equation under certain assumptions on the electromagnetic material parameters. The second central result, a uniqueness theorem, is proven by a variational argumentation and again depends on the values of the electromagnetic material parameters. In the main part of this thesis, we then extend the considered obstacles to “real” multilayered obstacles consisting of at least two grating interfaces. For these, we propose two recursive integral equation algorithms to determine the generated reflected and transmitted waves. On the one hand, the recursive scattering matrix method and, on the other hand, a recursive algorithm based on the transmission conditions across the interfaces of the multilayered structure. In addition to their accurate derivation, new existence and uniqueness results, depending on the electromagnetic properties of the considered obstacle, are presented for each algorithm. Their proofs partially exploit the insights originating from the treatment of the single interface model problem. Our analytical investigation is intended to provide a basis for new efficient numerical implementations of the biperiodic multilayered electromagnetic scattering problem.

Despite the high potential of geothermal reservoirs in Meshkinshahr, we only see the government entering the electricity extraction of geothermal energy because the cost of the Meshkinshahr geothermal electricity is higher than the balanced price of the electricity market and the private sector is disadvantaged for entering it. So, the government has adopted a feed in tariff policy for geothermal electricity to encourage private sector investors. This research is aimed at financial appraisal of Maskinshahr geothermal power plant with the assumption of feed in tariff by the government with Equivalent Uniform Annual Worth, Equivalent Uniform Annual Worth, and Equivalent Uniform Annual Cost methods. Equivalent Uniform Annual Benefit is obtained from feed in tariff of government and Equivalent Uniform Annual Cost is determined based on technical and economic components of the geothermal power plant and macroeconomic parameters. The results of the data analysis show that the construction of the geothermal power plant is fully justified with the 14% reduction rate, but if the investor's minimum expected rate exceeds 54%, the construction of the power plant has no economic justification. Also, if the construction of Meshkinshahr geothermal plant takes more than 13 years and 5 months like the government project, the generation of geothermal power is not cost-effective.

According to prospects of international organisations like OECD and FAO, Ukraine will be one of the important suppliers of agricultural products on the world market in the coming decade. Thus, Ukrainian agricultural production and exports are important elements in sustaining global food security. However, the country threatens global food security as well as its own agricultural development when applying grain export restrictions, as happened several times in recent years. Therefore, any impediments to grain trade in the country should be carefully inspected. In this paper we analyse recent developments of Ukrainian agricultural policy influencing grain trade. We show that any export restriction brings large welfare losses compared to a free trade situation. We support our claim by a comparative analysis of the different export policies applied by the Ukrainian government on the domestic wheat market between 2006 and 2014. Additionally, we suggest and discuss alternative policy responses to realise the policy goal of domestic food security. As the policies applied, export tax, export quota and tax reimbursement, cannot be compared directly we quantify the tax equivalent of each trade policy measure. Under a set of specific assumptions the tax equivalent can be used to compare the effects of policies theoretically and empirically. Our findings go along with theory and show that export quotas in 2006 and in 2010 had a more restrictive effect on export than export taxes in 2011. Effects of non-reimbursement of VAT are very close to the effects of export tax in 2011 (at the level of 9%), mainly because most of the time these two measures were implemented simultaneously. We also calculated tariff equivalent of VAT non-reimbursement excluding the period of export taxes. Based on these results, the measure corresponds to a slight decline of the tariff equivalent in absolute terms. As an alternative policy option for the Ukrainian government to respond more efficiently to increasing world market prices in the future it is advised to use consumer-oriented measures for the most vulnerable groups of people instead of distorting market mechanisms.

Typed feature logics have been employed as description languages in modern type-oriented grammar theories like HPSG and have laid the theoretical foundations for many implemented systems. However, recursivity pose severe problems and have been addressed through specialized powerdomain constructions which depend on the particular view of the logician. In this paper, we argue that definite equivalences introduced by Smolka can serve as the formal basis for arbitrarily formalized typed feature structures and typed feature-based grammars/lexicons, as employed in, e.g., TFS or TDL. The idea here is that type definitions in such systems can be transformed into an equivalent definite program, whereas the meaning of the definite program then is identified with the denotation of the type system. Now, models of a definite program P can be characterized by the set of ground atoms which are logical consequences of the definite program. These models are ordered by subset inclusion and, for reasons that will become clear, we propose the greatest model as the intended interpretation of P, or equivalent, as the denotation of the associated type system. Our transformational approach has also a great impact on nonmonotonically defined types, since under this interpretation, we can view the type hierarchy as a pure transport medium, allowing us to get rid of the transitivity of type information (inheritance), and yielding a perfectly monotonic definite program.

The bacteria that often cause infectious diarrhea are Escherichia coli and Shigella dysenteriae. Excessive and less rational use of antibiotics in diarrhea cases encourages the development of multi drug pathogen resistance. Propolis is one solution to overcome diarrheal infections. The purpose of this study was to determine the ability of the antibacterial effects of propolis extract on Escherichia coli and Shigella dysenteriae bacteria in in vitro testing with various concentrations. Research in laboratory experiments in vitro. The sample in this study was the bacteria Escherichia coli and Shigella dysenteriae with the stages of research starting from the extraction process carried out using a multilevel extraction method. The results showed that the smallest concentration of n-hexane fraction which still inhibited the growth of Escherichia coli and Shigella dysenteriae bacteria was 250 µg / ml and this concentration was expressed as KHM value. The equality test of 250 µg / ml n-hexane propolis fraction was equivalent to 4.0 µg / ml ciprofloxacin to Escherichia coli and equivalent to 4.6 µg / ml ciprofloxacin against Shigella dysenteriae, while the equality test concentration of 250 µg / ml ethyl acetate propolis equivalent to 5.2 µg / ml of ciprofloxacin against Escherichia coli and equivalent to 4.5 µg / ml of ciprofloxacin against Shigella dysenteriae. The conclusion of this study is that n-hexane extract and ethyl acetate propolis have antibacterial effectiveness against Escherichia coli and Shigella dysenteriae. The n-hexane and ethyl acetate propolis fractions have lower antibacterial activity compared to ciprofloxacin in inhibiting the growth of Escherichia coli and Shigella dysenteriae. Antibacterial compounds contained in the n-hexane fraction and ethyl acetate propolis are flavonoids and phenol

[K(2)(P(4)Mes(4))] (1) or [Na(2)(THF)(4)(P(4)Mes(4))] (2) (Mes = 2,4,6-Me(3)C(6)H(2)) reacts with one equivalent of HCl and subsequently with 0.5 equivalents of [{RhCl(cod)}(2)] (cod = 1,5-cyclooctadiene) to give a mixture of rhodium complexes, from which [Rh(P(4)HMes(4))(cod)] (3) and the secondary product [Rh(2)(micro-P(2)HMes(2))(mu-PHMes)(cod)(2)] (4) were isolated and characterised by X-ray diffraction studies. Alternatively, the reaction of [K(2)(P(4)Ph(4))] (5) or [Na(2)(THF)(5)(P(4)Ph(4))] (6) with one equivalent of HCl and subsequently with one equivalent of [CuCl(PCyp(3))(2)] (Cyp = cyclo-C(5)H(9)) gave the complex [Cu(4)(P(4)Ph(4))(2)(PH(2)Ph)(2)(PCyp(3))(2)] (7), presumably via disproportionation of the monoanion (P(4)HPh(4))(-).