Main Proof Research Articles

Grothendieck rings of theories of modules

The model-theoretic Grothendieck ring of a first order structure, as defined by Krajicěk and Scanlon, captures some combinatorial properties of the definable subsets of finite powers of the structure. In this paper we compute the Grothendieck ring, K0(MR), of a right R-module M, where R is any unital ring. As a corollary we prove a conjecture of Prest that K0(MR) is non-trivial, whenever M is non-zero. The main proof uses various techniques from simplicial homology and lattice theory to construct certain counting functions.

Synchronization of fractional-order different memristor-based chaotic systems using active control

In this article, synchronization of two different fractional-order memristor-based chaotic systems is considered. To achieve synchronization, an active control technique is used. The main proof is concerned with the problem of synchronization of memristor-based Lorenz systems with memristor-based Chua’s circuits. Numerical simulations of fractional-order memristor-based chaotic systems are performed by using the Caputo version and a predictor–corrector algorithm for fractional-order differential equations, which is a generalization of the Adams–Bashforth–Moulton method. From the simulations, it will be verified that the proposed control method is effective in achieving synchronization.

A collapse theorem for holographic algorithms with matchgates on domain size at most 4

Holographic algorithms with matchgates are a novel approach to design polynomial time computation. They use Kasteleyn's algorithm for perfect matchings, and more importantly a holographic reduction. The two fundamental parameters of a holographic reduction are the domain size k of the underlying problem and the basis size ℓ. A holographic reduction transforms the computation to matchgates by a linear transformation that maps to (a tensor product space of) a linear space of dimension 2ℓ. We prove a sharp basis collapse theorem, which shows that for domain size 3 and 4, all non-trivial holographic reductions can be expressed with a basis of size 1 or 2, respectively. The main proof techniques are Matchgate Identities and a Group Property of matchgate signatures.

Roll Hemming Based Innovative Assembly System for Automotive Products

This work reports an investigation on an innovative assembly system for the components of a coolant pump designed for automotive industry. After having identified the main parameters involved in the process, the authors develop a numerical model aimed to investigate the main characteristics of the process which has been subsequently validated experimentally. To do this a simple mock-up of the pump was built that was employed for roll hemming tests and then to the main proof tests to assess the functionality of the assembled product. Experimental tests were conducted on some specimens in order to check the quality of the assembly between parts. The specimens passed the leak test as well as the torque proof as required by the design specifics which prove the validity and feasibility of this type of process.

Irremissible stimulate on ‘Unified fixed point theorems in fuzzy metric spaces via common limit range property’

Abstract One of the goals of this short note is to alert researchers as regards some mistakes that appeared in a recent paper (Chauhan, Khan and Kumar in J. Inequal. Appl. 2013:182, 2013). This entails main proofs based on a false result, which invalidates all statements. We also give a complete revision of the antecedents of this work in order to find the main reasons of the mistakes. Finally, the main aim of this note is to propose a correct, more general version of the main theorems in the paper mentioned.

Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches \boldmath2𝜋 and completion of the main proof

This is the third and final article in a series which prove the fact that a K-stable Fano manifold admits a Kähler-Einstein metric. In this paper we consider the Gromov-Hausdorff limits of metrics with cone singularities in the case when the limiting cone angle approaches 2 π \pi . We also put all our technical results together to complete the proof of the main theorem.

Avicenna’s Corporeal Form and Proof of Prime Matter in Twelfth-Century Critical Philosophy: Abū l-Barakāt, al-Masʿūdī and al-Rāzī

This article explores a previously unknown twelfth-century debate surrounding Avicenna’s theory of matter, in particular his views that, being deprived of actuality, prime matter is non-corporeal, and that body is invested with corporeity by a substantial form impressed into matter known as corporeal form. Avicenna’s main proof of prime matter from body’s susceptibility to division was targeted earlier in the century by Abū l-Barakāt al-Baghdādī and Sharaf al-Dīn al-Masʿūdī, but was later reinterpreted and developed by Fakhr al-Dīn al-Rāzī, who brought this particular debate to a close. The problem, however, persisted as a puzzle that exercised later Arabic philosophers.

Steady-state $GI/G/n$ queue in the Halfin–Whitt regime

We consider the FCFS $\mathit{GI}/\mathit{GI}/n$ queue in the so-called Halfin-Whitt heavy traffic regime. We prove that under minor technical conditions the associated sequence of steady-state queue length distributions, normalized by $n^{1/2}$, is tight. We derive an upper bound on the large deviation exponent of the limiting steady-state queue length matching that conjectured by Gamarnik and Momcilovic [Adv. in Appl. Probab. 40 (2008) 548-577]. We also prove a matching lower bound when the arrival process is Poisson. Our main proof technique is the derivation of new and simple bounds for the FCFS $\mathit{GI}/\mathit{GI}/n$ queue. Our bounds are of a structural nature, hold for all $n$ and all times $t\geq0$, and have intuitive closed-form representations as the suprema of certain natural processes which converge weakly to Gaussian processes. We further illustrate the utility of this methodology by deriving the first nontrivial bounds for the weak limit process studied in [Ann. Appl. Probab. 19 (2009) 2211-2269].

Persistent asymmetric password-based key exchange

Abstract. Asymmetric password based key exchange is a key exchange protocol where a client and a server share a low entropic password while the server additionally owns a high entropic secret with respect to a public key. There are simple solutions for this, e.g., [ACM Trans. Inf. Syst. Secur. 2 (1999), 230–268] and its improvement in [Proceedings of CCS 1999, ACM (1999), 63–72]. In the present paper, we consider a new threat to this type of protocol: if a server's high entropic secret gets compromised (e.g., due to cryptanalysis or a poor management), the adversary might quickly break lots of passwords and cause uncountable damage. In this case, one should not expect the protocol to be secure against an off-line dictionary attack since, otherwise, the protocol is in fact a secure password-only key exchange by making the server high entropic secret public. Of course a password-only key exchange does not suffer from this threat as the server does not have a high entropic secret at all. However, known password-only key exchange protocols are not very efficient (note: we only consider protocols without random oracles). This motivates us to study an efficient and secure asymmetric password key exchange that avoids the new threat. In this paper, we first provide a formal model for the new threat, where essentially we require that the active adversary can break ℓ $\ell $ passwords in α ℓ | 𝒟 | $\alpha \ell |\mathcal {D}|$ steps (for α < 1 / 2 $\alpha <1/2$ ) only with a probability negligibly close to exp ( - β ℓ ) $\exp (-\beta \ell )$ for some β > 0 $\beta >0$ , where 𝒟 $\mathcal {D}$ is a password dictionary. Then, we construct a framework of asymmetric password based key exchange. We prove that our protocol is secure in the regular model where server high entropic key is never compromised and that it prevents the new threat. To do this, we introduce a new technique by abstracting a probabilistic experiment from the main proof and providing a neat analysis of it.

Mean field conditions for coalescing random walks

The main results in this paper are about the full coalescence time $\mathsf{C}$ of a system of coalescing random walks over a finite graph $G$. Letting $\mathsf{m}(G)$ denote the mean meeting time of two such walkers, we give sufficient conditions under which $\mathbf{E}[\mathsf{C}]\approx 2\mathsf{m}(G)$ and $\mathsf{C}/\mathsf{m}(G)$ has approximately the same law as in the "mean field" setting of a large complete graph. One of our theorems is that mean field behavior occurs over all vertex-transitive graphs whose mixing times are much smaller than $\mathsf{m}(G)$; this nearly solves an open problem of Aldous and Fill and also generalizes results of Cox for discrete tori in $d\geq2$ dimensions. Other results apply to nonreversible walks and also generalize previous theorems of Durrett and Cooper et al. Slight extensions of these results apply to voter model consensus times, which are related to coalescing random walks via duality. Our main proof ideas are a strengthening of the usual approximation of hitting times by exponential random variables, which give results for nonstationary initial states; and a new general set of conditions under which we can prove that the hitting time of a union of sets behaves like a minimum of independent exponentials. In particular, this will show that the first meeting time among $k$ random walkers has mean $\approx\mathsf{m}(G)/\bigl({\matrix{k 2}}\bigr)$.

The New Cosmology Rrising from the Quantum Pushing Gravity Interaction—The Case of Accelerating Universe

In 2011 three astronomers were awarded the Nobel Prize for Physics having focussed a correct method of measuring cosmic distances by observation of far Supernovae Ia. Assuming the 'lambda’CDM expanding model, they showed that part of the Universe was accelerating, contrary to the original General Relativity predictions. The acceleration was attributed to an Obscure energy linked to the cosmological constant L. This constasnt was formerly introduced by Einstein in the original G.R. equations to empirically counterbalance the gravitational force to the aim of describing the (known) static universe. After the Hubble’s discovery (1929) of galaxy redshifts, which launched the expanding universe, Einstein rejected L. This was the sign that he considered L a provisional parameter, not the expression of a new physical force. Nevertheless, this parameter is till today taken into account by cosmologists to fit their observations through the LCDM model. Something is not consequent in the history of the Gravitational theory. The “accelerated expansion” of the universe can be firmly established only through a model independent way. In fact the SNe distances calculated by LCDM expanding model resulted so large that part of the SNe exploded before the so called Big bang Age, in contrast with the bases of the expansion. The astronomers appear reluctant to claim this splashing result. Something in the Obscure energy is not convincing. Before knowing the astronomer’s work, I carried out a research about the physical inadequacy of General Relativity as proper theory of Gravitation, notwithstanding the great success in astronomical observations. The profound reason of this inconsistency is the absence of interaction-waves, contrarily to other fundamental Interactions considered in the Standard Model. From several decades the research attempted to improve this unsatisfactory situation trying to detect the so called gravitational waves coming from cosmic events, but no tangible results have been obtained yet. Actually, the gravitational-inertial waves surely exist, as well as the measured gravitational force. The wavelength I found is of the order of the Planck’s length, so adequate tools are necessary for detection. One year ago I published a comprehensive analysis which, recognising the inadequacy of the old kinematic basis of Special relativity, gave rise (Michelini, 2012) to a Relativistic Dynamics re-founded on the new dynamical basis of the Micro-quanta paradigm. The high flux fo of micro-quanta filling the space originates, through the mutual-shielding between two particles/masses, the Quantum Pushing gravitational force, whereas at very short distances (<10-15) the same flux fo generates the Strong and Weak nuclear forces. Contrarily to the old Newton’s ideas, all these drawing forces do not pull the particles, but push them each other, thus giving rise to the process of Unification of forces. The present paper deals in particular with the Quantum Pushing Gravitation operating on large distances (cosmology), so that between two very distant masses the effect of the mutual scattering on the interposed micro-quanta is not negligible, giving rise to an attenuation factor on the gravitational constant. Quantum Pushing gravitation defines a variable G(r) = G exp(–Sor) showing that parts of Universe at cosmological distances? do not feel sensibly the gravitational force. Then the Universe results static, i.e. not expanding. The observed high Hubble’s redshifts depend on the interaction of photons that travelled across the micro-quanta giving rise to the redshift z(x) = exp(x/Lo) –1. The SNe measuring method just discovered exponentially increasing redshifs. Trying to explain this fact, the redshfts were introduced in the LCDM expanding model that produced the large distances resembling an accelerating universe. Several SNe resulted to exist well before the Big bang. Considering this contrast, which inhibits the expanding models, we introduced the observed SNe redshifts in the Static model, finding that the last SNa (z = 1.91) explosion happened 15 Gys ago, a reasonable result. Attributing the Hubble’s redshift to the Doppler appears no longer necessary. The static universe, immersed within the micro-quanta, is obviously evolving because the synthesis of heavy nuclei always occurs within the star cores. No arbitrary constant L has to be introduced in the Static model since the erroneous concept of “gravitational” mass has been previously eliminated through the Quantum Pushing gravity. The main proof of the Static model is the quantitative recognition that the observed Cosmic Microwave Background is due to redshifted photons emitted–with the characteristic black body spectrum–from all stars of the universe.

On the Lagrange multiplier theorem in Banach spaces

This article develops a new proof for the Lagrange Multiplier Theorem for optimization in Banach Spaces. The results are based on standard tools of analysis. We highlight the main theorem proof is obtained through an iterative process similarly to the essential contraction mapping theorem basic idea. Finally, in the last section, we address problems including inequality constraints as examples of the main result applications.

Stability regions for linear fractional differential systems and their discretizations

This paper concerns with basic stability properties of linear autonomous fractional differential and difference systems involving derivative operators of the Riemann–Liouville type. We derive stability regions for special discretizations of the studied fractional differential systems including a precise description of their asymptotics. Our analysis particularly shows that discretizations based on backward differences can retain the key qualitative properties of underlying fractional differential systems. In addition, we introduce the backward discrete Laplace transform and employ some of its properties as the main proof tool.

Le roman vietnamien francophone: orientalisme, occidentalisme et hybridité by Ching Selao

Roy shares Girard’s belief in the explanatory power of the concept of mimetic desire or mediated desire: we learn what to want by observing what others prize, as do the male victims of Freud’s Oedipus complex who desire their mother because they see their father desiring her (today, the increasing numbers of LGBT parents successfully raising ‘normal’ children who experience heterosexual desire suggest that both Freud’s and Girard’s views must be qualified). Of course, Girard’s concept of desire extends far beyond sexuality to other worldly goods such as wealth, power, and social status, as Pierre Bourdieu’s classic Distinction suggests. But Girard believes fictional characters can become free only through a religious revelation. Dostoevsky, his starting point, provides him with many apposite examples. Roy eventually finds Girard ‘too clear’ (41–75)–—in a word, reductive. He rereads Girard’s main proof texts—Don Quixote, Balzac, Flaubert’s three bourgeois novels, Proust, and the apparent counter-example of Valéry’s Monsieur Teste—to counterbalance Girard both with Mikhaïl Bakhtine, who emphasizes the freedom and indeterminacy of fictional characters, and also with a nuanced view of Henri Bergson’s theory of the comic. Roy explains that Bergson’s definition of comedy as ‘a mechanism stuck onto a living person’ works to explain why we laugh only because we perceive incongruity: the fool’s incorrigible repetition of a dysfunctional behavior together with the fool’s humanity. Roy’s ultimate model for understanding fiction is Milan Kundera, an excellent choice of a great writer who is also a great critic. One cannot begin to do justice to Roy’s judicious, wide-ranging, and incisive study in a brief review. Nearly every analysis of a critical or fictional work rewards the reader (he does not show us much new concerning Flaubert). His clear style makes him agreeable to read; his frequent teacherly recapitulations make his arguments easy to follow. His powers of synthesis are noteworthy, and he skillfully unfolds an ever-widening vision that begins by his appearing to be a disciple of Girard, and ends with his realization that the history of the novel is not a road toward a destination determined in advance, but a wandering path. In conclusion, he offers us a two-fold view. First he returns to Don Quixote to demonstrate how, despite Don Quixote’s deathbed conversion to common sense, Cervantes preserves the ambiguity that preserves the novel’s refreshing humor even long after his satiric targets—the knight-errant and Romances of Chivalry— have disappeared from our culture. Then Roy slyly concludes that the problem of excessive clarity is not peculiar to Girard, but to the genre of the essay in general: “On ne peut manier des concepts sans chercher à dissoudre des contradictions, et dès lors se voir obligé, face à celles qui résistent [... à] en être réduit à osciller soim ême entre les deux termes qui les constituent et, par ce mouvement même, à tourner sans cesse le dos à l’humour” (270). Michigan State University Laurence M. Porter SELAO, CHING. Le roman vietnamien francophone: orientalisme, occidentalisme et hybridité. Montréal: PU de Montréal, 2011. ISBN 978-2-7606-2222-7. Pp. 215. $34,95 Can. Née vers 1910, la littérature vietnamienne francophone demeure méconnue, malgré la présence de Franco-Vietnamiennes (Lefèvre, Lê, Moï) sur la scène 1274 FRENCH REVIEW 86.6 littéraire contemporaine. Depuis les travaux de Yaeger, pionnier des années 80, peu de chercheurs se sont penchés dessus. Notons plusieurs lignes directrices au travail de Selao. Elle se concentre sur l’étude de romans qui traitent du choc des cultures mais sont écrits par des auteurs vietnamiens, et non européens. Si elle reconnaît que les formations discursives sont liées à des contextes de colonisation, décolonisation et postcolonisation, pour elle, l’orientalisme et l’occidentalisme sont deux types de discours pétrifiants: elle remet en question les binarismes des discours successifs sur l’Autre, les oppositions qui “hantent toutes les visions du monde” (16). Ses analyses de romans démontrent que l’évolution des discours sur l’orientalisme , l’occidentalisme et l’hybridité n’est pas forc...

WOMEN’S RIGHTS TO SUCCESSION IN UNREGISTERED MARRIAGES: A REFERENCE TO THE INSTRUMENT OF WAṢIYYAH

It is an essential requirement for a marriage to be registered according to the procedures as provided by the law. Non-registration of a marriage leads to the non-availability of a marriage certificate, being the main proof of the existence of the marital relationship. This situation results in various legal complications in claiming the rights, including a right to property under the law of succession which arises upon the death of the spouse. Such a right, even though guaranteed by the Sharīʿah, is not recognized by Malaysian law. This article seeks to examine women’s rights to succession in cases of unregistered marriage with special reference to the execution of a waṣiyyah as a useful instrument to protect the rights of the unregistered wives against husbands’ estates.

Strict stability in terms of two measures for impulsive differential equations with ‘supremum’

Strict stability for a nonlinear system of impulsive differential equations with ‘supremum’ is defined and studied. Razhumikhin method with piecewise continuous scalar Lyapunov functions and comparison results for scalar impulsive differential equations are the bases of the main proofs. To unify a variety of stability concepts and to offer a general framework for the investigation of the stability theory, the notion of stability in terms of two measures has been applied. An example illustrating the usefulness of the obtained sufficient conditions is also included.

Application of electrochemical impedance spectroscopy and conventional rebinding experiments for the investigation of recognition characteristic of bulky and nano-sized imprinted polymers

In this work, recognition of target molecules by nano- and micro-sized molecularly imprinted polymers (nano-MIP and micro-MIP) was investigated by using electrochemical impedance spectroscopy (ESI). Modification of carbon paste electrode (CP) with promethazine (PMZ)-imprinted and non-imprinted polymers (MIP and NIP) influenced its ESI behavior, in both low and high frequency regions, approximately in the same manner. However, adsorption of target molecules on the electrodes, modified with different polymeric materials, influenced dissimilarly their ESI behaviors. Target molecules adsorption decreased bulk resistance of the MIP-based electrodes, whereas sorption of cross-reactant molecule increased this parameter of the electrode. This effect for bulky MIP-based electrode was more than that for the nano-MIP electrode. Swelling of the MIP materials, after target molecule recognition, was proposed as a main proof for this observation. However, bulk resistance of the NIP-based electrodes increased with adsorption of both target and foreign molecule. Swelling experiment indicated that in the presence of an organic solvent the bulky MIP particles expanded more than the nano-sized MIP. This led to erased memory effect in the bulky MIP. Scatchard plot showed that the recognition sites of the nano-sized MIP particles had more affinity to target molecule, compared to those of the bulky MIP particles. The prepared MIP based electrodes were used to plot the calibration curves based on the variation of bulk resistance of the electrodes versus PMZ concentration. Although, the MIP nanoparticles showed higher affinity for the target molecule the bulky MIP-based electrode was capable to determine target molecule at lower concentrations.

The development of executive function

Executive function is a group of the higher-order cognitive abilities that coordinate and monitor other abilities and behavior. As complex cognitive functio­ning is primarily attributed to adults, executive function in children has rarely been studied. However, research of executive function from the perspective of develo­pmental psychology and psychopathology has become more frequent in recent decade. Several findings have attributed to this change, the discovery of an intriguing connection between children’s executive function and theory of mind among them. Several reviews have been published in the field, providing the detailed developmental map of most often studied components of executive function (Garon et al., 2008; Best et al., 2009). However, they touch less on the broader context of executive function development. The aim of this review paper is to discuss the main findings, new trends and unanswered questions associated with developmental research in executive function, hoping this will stimulate Lithuanian psychologists become more involved in the field.We start the first part of the paper by discussing the difficulties in developmental research of executive function associated with the theoretical ambiguity of the construct and methodological problems. Most authors have focused to three main executive functions in recent years: mental set shifting, working memory updating and response inhibition. However, none of the neuropsychological tests measure isolated component of executive function, which makes the interpretation of the findings complicated. Studying executive function in young children at least partly addresses this problem, as the neuropsychological tasks are less complex, so more “pure” in this group. We briefly describe the developmental trends of main executive functions, concluding that the development of these abilities starts as early as the first year of life, undergoes the biggest changes in preschool years and continues till late childhood and even adulthood. We finally outline the importance of studying psychosocial context of the development of executive function. There is evidence that early social interaction may affect the development of executive function (Bibok et al., 2009; Bernier et al., 2010), but much remains to be done to better understand the mechanisms of the development of these functions. The second part of the paper is devoted to the connection between the development of executive function and theory of mind. There are four main proofs of this connection: 1) positive correlation between the executive function and theory of mind test results; 2) matching developmental paths of these two psychic functions; 3) matching brain regions; 4) disorders of both psychic functions in case of psycho­pathology (autism disorder in particular). Although the connection between executive function and theory of mind development is well documented, little is known about the nature and direction of this connection. The most prominent hypothesis is that executive function development stimulates the emergence of executive function (Carlson et al., 2004; Hughes and Ensor, 2007), but alternative explanations exist. We suggest that the explanations taking into account the social context of the development of both psychic functions should be considered.

Foundation and generalization of the expansion by regions

The "expansion by regions" is a method of asymptotic expansion developed by Beneke and Smirnov in 1997. It expands the integrand according to the scaling prescriptions of a set of regions and integrates all expanded terms over the whole integration domain. This method has been applied successfully to many complicated loop integrals, but a general proof for its correctness has still been missing. This paper shows how the expansion by regions manages to reproduce the exact result correctly in an expanded form and clarifies the conditions on the choice and completeness of the considered regions. A generalized expression for the full result is presented that involves additional overlap contributions. These extra pieces normally yield scaleless integrals which are consistently set to zero, but they may be needed depending on the choice of the regularization scheme. While the main proofs and formulae are presented in a general and concise form, a large portion of the paper is filled with simple, pedagogical one-loop examples which illustrate the peculiarities of the expansion by regions, explain its application and show how to evaluate contributions within this method.

Uniqueness and regularity for a system of interacting Bessel processes via the Muckenhoupt condition

We study the regularity of a diusion on a simplex with singular drift and reflecting boundary condition which describes a finite system of particles on an interval with Coulomb interaction and reflection between nearest neighbors. As our main result we establish the strong Feller property for the process in both cases of repulsion and attraction. In particular the system can be started from any initial state, including multiple point configurations. Moreover we show that the process is a Euclidean semi-martingale if and only if the interaction is repulsive. Hence, contrary to classical results about reflecting Brownian motion in smooth domains, in the attractive regime a construction via a system of Skorokhod SDEs is impossible. Finally, we establish exponential heat kernel gradient estimates in the repulsive regime. The main proof for the attractive case is based on potential theory in Sobolev spaces with Muckenhoupt weights.