Present Proof Research Articles

Multi-level coupled cluster theory.

We present a general formalism where different levels of coupled cluster theory can be applied to different parts of the molecular system. The system is partitioned into subsystems by Cholesky decomposition of the one-electron Hartree-Fock density matrix. In this way the system can be divided across chemical bonds without discontinuities arising. The coupled cluster wave function is defined in terms of cluster operators for each part and these are determined from a set of coupled equations. The total wave function fulfills the Pauli-principle across all borders and levels of electron correlation. We develop the associated response theory for this multi-level coupled cluster theory and present proof of principle applications. The formalism is an essential tool in order to obtain size-intensive complexity in the calculation of local molecular properties.

Environmental invitingness for transport-related cycling in middle-aged adults: A proof of concept study using photographs

IntroductionCurrent evidence on associations between modifiable environmental characteristics and transport-related cycling remains inconsistent. Most studies on these associations used questionnaires to determine environmental perceptions, but such tools may be subject to bias due to unreliable recall. Moreover, questionnaires only measure separate environmental characteristics, while real environments are a combination of different characteristics. To overcome these limitations, the present proof of concept study used panoramic photographs of cycling environments to capture direct responses to the physical environment. We examined which depicted environmental characteristics were associated to environments’ invitingness for transportation cycling. Furthermore, interactions with gender and participants’ cycling behavior were examined. MethodsFifty-nine middle-aged adults were recruited through purposeful convenience sampling. During a home visit, participants took part in a structured interview assessing demographics and PA during the preceding seven days, followed by an intuitive choice task and a (cognitive) rating task, which both measured 40 photographed environments’ invitingness to cycle along. Multi-level cross-classified analyses were conducted using MLwiN 2.26. ResultsBoth tasks’ multivariate results showed that presence of vegetation was identified as the most important environmental characteristic to invite people for engaging in transportation cycling, even when the amount of vegetation was relatively small. In the bivariate analyzes, some differences between results of the cognitive rating task and the intuitive choice task were found, showing that invitingness measured by the rating task was associated with environmental maintenance and cycling infrastructure, whereas invitingness determined by the choice task was associated with more traffic-oriented characteristics. Moreover, only for the choice task’s results, moderating effects of gender and participants’ cycling behavior in the preceding week were observed. ConclusionThe present study provides proof of concept that capturing people’s less cognitive, more intuitive responses to an environment’s invitingness for transport-related cycling may be important for revealing environment-behavior associations. If replicated in future studies using larger samples, results of our innovative measurements with photographs, especially those on vegetation, can complete the existing knowledge on which environmental characteristics are important for transportation cycling in adults and could form a basis to inform health promoters and local policy makers. However, future studies replicating our study method in larger samples and other population subgroups are highly encouraged. Moreover, causal relationships should be explored.

Microenvironmental pH measurement during sodium naproxenate dissolution in acidic medium by UV/vis imaging

Variable dissolution from sodium salts of drugs containing a carboxylic acid group after passing the acidic environment of the stomach may affect oral bioavailability. The aim of the present proof of concept study was to investigate pH effects in relation to the dissolution of sodium naproxenate in 0.01M hydrochloric acid. For this purpose a UV/vis imaging-based approach capable of measuring microenvironmental pH in the vicinity of the solid drug compact as well as monitoring drug dissolution was developed. Using a pH indicating dye real-time spatially resolved measurement of pH was achieved. Sodium naproxenate, can significantly alter the local pH of the dissolution medium, is eventually neutralized and precipitates as the acidic species naproxen. The developed approach is considered useful for detailed studies of pH dependent dissolution phenomena in dissolution testing.

Circle actions in geometric quantisation

The aim of this article is to present unifying proofs for results in geometric quantisation with real polarisations by exploring the existence of symplectic circle actions. It provides an extension of Rawnsley's results on the Kostant complex, and gives an alternative proof for Sniatycki's and Hamilton's theorems; as well as, a partial result for the focus-focus contribution to geometric quantisation.

Fugu for Logicians

What do you get when you cross a fallacy with a good argument? A fugu, that is, a valid argument that tempts you to reach its conclusion invalidly (named after the dangerous but delicious Japanese puffer fish). You have yielded to the temptation more than you realize. If you are a teacher, you may have served many fugus. They arise systematically through several mechanisms. Fugus are interesting intermediate cases that shed light on the following issues: bare evidentialism, false pleasure, philosophy of education, and the ethics of argument. Normally, a fugu will not yield knowledge from known premises. But if the reasoning is only slightly fallacious, they do yield knowledge. These mild fugus show that we can gain knowledge by invalid reasoning. This is a conservative resource for historians. They want to credit discoveries to Euclid rather than those who made minor corrections to his proofs, such as David Hilbert. We also benefit from this practice of grandfathering in old standards of knowledge attribution. For we can compete spiritedly for priority. We do not need to worry that credit will instead go to future scholars who will make the minor amendments needed to raise present proofs to a future standard of demonstration.

O potrzebie, a nawet konieczności uwzględnienia infiksów w opisie polskiej fleksji werbalnej

The aim of this paper is to present proof that infixes, being markers of the perfective aspect, exist in Polish verbal inflection. At the same time, it is demonstrated that some Polish, and more generally, Slavic affixes, constitute better examples of infixes than those that have been appearing in coursebooks and encyclopaedias of general linguistics so far. Moreover, it is suggested that there is a possibility of t including infixes in descriptions of inflections of certain Germanic languages.

ABSTRACT 697

Background and aims: Valproate, frequently used anti-epileptic in childhood, may also present dramatic proof of...hemorrhage! We present a case report of a peculiar (and dangerous) drug interaction. Aims: We report on a newborn with severe factor VII deficiency. While decreasing doses of Novoseven ® by the age of 40 days, seizures revealed intracranial hemorrhage, and infant is put under Valproate (VPA) at 20 mg/kg/day. Therefore, he has two further episodes followed by intraperitoneal bleedings despite prophylaxis with recombinant Factor VII. At his 4th month, normal EEG (and good psychomotor development) allowed interrupting valrpoate, with no more such severe hemorrhage. The boy is now aged 12 months and is free of notable neurological disorders. Methods: Valproate is widely prescribed for focal and generalized seizures. Its toxicities are well established: teratogenic, hepatic, pancreatic and hematologcal; and induced coagulopathies may present with a myriad of disturbances: platelet disorders, acquired deficit in Factor von Willebrand and lower PT, CKT, fibrin or factor XIII Exceptionally, falling levels of factors VII have been associated. Our case, after exhaustive search PubMed and Google Scholar, seems to be the third. Results: Fortunately, most children-like our patient-responded to the suspension of VPA This brings out precautions in drug interactions: rereading of the monographs of these drugs did not mention this contra-indication. Conclusions: Valproate, commonly used in children, is not devoid of hematological risk. Its use in patients with pre-existing coagulopathies must be carefully weighed and regularly reviewed.

Elementary proofs of Radu and Sellers’ results for broken 2-diamond partitions

In 2007, Andrews and Paule introduced a new class of combinatorial objects called broken k-diamonds. Let Δk(n) be the number of broken k-diamonds partitions of n. By using MacMahon’s partition analysis, they found that the generating function of Δk(n) is an infinite product, which attracted many mathematicians to study its congruence properties. Recently, Radu and Sellers found infinitely many Ramanujan-like congruences modulo 3 for Δ2(n). In fact, they obtained 3-dissections of the generating function for Δ2(n) modulo 3 by using the theory of modular forms. In this brief note, we aim to present elementary proofs of Radu and Sellers’ results by using several theta function identities due to Ramanujan.

Process Authentication for High System Assurance

This paper points out the need in modern operating system kernels for a process authentication mechanism, where a process of a user-level application proves its identity to the kernel. Process authentication is different from process identification. Identification is a way to describe a principal; PIDs or process names are identifiers for processes in an OS environment. However, the information such as process names or executable paths that is conventionally used by OS to identify a process is not reliable. As a result, malware may impersonate other processes, thus violating system assurance. We propose a lightweight secure application authentication framework in which user-level applications are required to present proofs at runtime to be authenticated to the kernel. To demonstrate the application of process authentication, we develop a system call monitoring framework for preventing unauthorized use or access of system resources. It verifies the identity of processes before completing the requested system calls. We implement and evaluate a prototype of our monitoring architecture in Linux. The results from our extensive performance evaluation show that our prototype incurs reasonably low overhead, indicating the feasibility of our approach for cryptographically authenticating applications and their processes in the operating system.

Proving empirical key-correlations in RC4

In view of the recent attacks on practical network protocols like WEP, WPA and TLS, there has been a renewed interest in the non-random behavior of RC4, the stream cipher that constitutes the core of all these protocols. While most of the non-random events in the cipher, more commonly known as ‘biases’, are initially reported as experimental observations, it is equally important to present theoretical proofs of such biases to justify the attacks based on these. In this paper, we provide theoretical proofs of all significant empirical correlations between the initial bytes of the RC4 keystream and its secret key, as experimentally observed by Sepehrdad, Vaudenay and Vuagnoux in SAC 2010.

Misconceptions in the use of the General Linear Model applied to functional MRI: a tutorial for junior neuro-imagers

This tutorial presents several misconceptions related to the use the General Linear Model (GLM) in functional Magnetic Resonance Imaging (fMRI). The goal is not to present mathematical proofs but to educate using examples and computer code (in Matlab). In particular, I address issues related to (1) model parameterization (modeling baseline or null events) and scaling of the design matrix; (2) hemodynamic modeling using basis functions, and (3) computing percentage signal change. Using a simple controlled block design and an alternating block design, I first show why “baseline” should not be modeled (model over-parameterization), and how this affects effect sizes. I also show that, depending on what is tested; over-parameterization does not necessarily impact upon statistical results. Next, using a simple periodic vs. random event related design, I show how the hemodynamic model (hemodynamic function only or using derivatives) can affects parameter estimates, as well as detail the role of orthogonalization. I then relate the above results to the computation of percentage signal change. Finally, I discuss how these issues affect group analyses and give some recommendations.

The complete proofs of optimal ordering policies for a retailer with up-stream and down-stream trade credits in a supply chain

Teng and Goyal (2007) consider optimal ordering policies for a retailer in a supply chain with up-stream and down-stream trade credits. Their inventory models are correct and interesting. However, processes of proofs and arguments of Theorems 1 and 2 in Teng and Goyal (2007) fill shortcomings such that validities of their proofs are questionable. From the viewpoint of logic, their proofs are not complete. So, the main purpose of this paper is to remove those shortcomings and present complete proofs for Teng and Goyal (2007).

Elementary proofs of parity results for broken 3-diamond partitions

Recently, Radu and Sellers studied the parity of the function Δ3(n) which counts the number of broken 3-diamond partitions. They found interesting relationships between the generating functions in question and certain eta products. In this note, we aim to present elementary proofs of these congruence relationships.

Collapse mechanisms and the existence of equilibrium solutions for masonry bodies

The equilibrium equations of no-tension (masonry-like) bodies are analyzed. Unlike the existing proofs of the existence of the solution by Anzellotti or Giaquinta and Giusti, the present proof does not employ the uniform safe load condition. It is based on the assumption of the absence of a suitably defined collapse mechanisms. The collapse mechanism belongs to a generalized space BD(cl Ω) of displacements of bounded deformation on the closure cl Ω of the body Ω. This generalized displacement can have a jump discontinuity on the boundary of the body and the generalized strain is a measure on the closure of the body (instead of the standard interpretation as a measure supported by the interior). The equilibrium solution, however, belongs to the classical space of displacements of bounded deformation BD(Ω).

Evaluation of Intracavity Optogalvanic Spectroscopy for Radiocarbon Measurements

Ever since the first publication of intracavity optogalvanic spectroscopy (ICOGS) in 2008, this novel technique for measuring the (14)C/(12)C ratio in carbon dioxide has rendered considerable attention. As a result, there are currently at least five different research groups pursuing research on ICOGS. With a claimed limit of detection of 10(-15) ((14)C/(12)C), i.e., in the same order as accelerator mass spectroscopy, achieved with a relatively inexpensive and uncomplicated table-top system, ICOGS has major scientific and commercial implications. However, during the past 5 years, no research group has been able to reproduce these results or present additional proof for ICOGS's capability of unambiguous (14)C detection, including the authors of the original publication. Starting in 2010, our group has set up a state-of-the-art ICOGS laboratory and has investigated the basic methodology of ICOGS in general and tried to reproduce the reported experiments in particular. We have not been able to reproduce the reported results concerning the optogalvanic signals dependence on (14)C concentration and wavelength and, ultimately, not seen any evidence of the capability of ICOGS to unambiguously detect (14)C at all. Instead, we have found indications that the reported results can be products of measurement uncertainties and mistakes. Furthermore, our results strongly indicate that the reported limit of detection is likely to be overestimated by at least 2 orders of magnitude, based on the results presented in the original publication. Hence, we conclude that the original reports on ICOGS cannot be confirmed and therefore must be in error.

On the optimal inventory policy for the EPQ model under trade credit

Huang and Huang [International Journal of Systems Science, 39 (2008), 539-546] use the algebraic method to determine the optimal inventory replenishment policy for the retailer in the extended model under trade credit. Recently, Chung [International Journal of Systems Science, 41 (2010), 1115-1120] presents the comments to overcome shortcomings and present complete proofs for Huang and Huang (2008). The main purpose of this note is to develop another proof to readers.

Structure of multi-wall carbon nanotubes: AA′ stacked graphene helices

The structure of multi-wall carbon nanotubes has been attributed previously to disordered stacking of the graphene planes. Evidence is presented that the nanotubes analyzed in this paper occur with stacked graphene layers in the sequence of AA′, where alternate graphene planes are translated by half the hexagon width. We further present proof that the crystalline materials comprise graphene helices (∼5 nm in width), rather than in the form of a perfect tube. We also show that the structural model proposed here may be a common structure for multi-wall carbon nanotubes.

57 Fe Mössbauer and X-ray characterisation of sandstones

Sandstones from the Free State province in South Africa have been mined and processed mainly by small scale and artisanal miners in the rural areas. In the present investigation basic fire proof and water absorption tests, X-ray and γ-ray based characterisation techniques were used to study the sandstones. The collected samples were grouped according to their apparent colour in day light conditions and the elemental analysis showed the presence of a high amount of oxygen (>52%) and silicon (>38%) with Mn, Al, Fe and Ca as major elements in proportions related to the colour distribution of the various sandstones. The uniaxial compressive stress was found to be the highest (56 MPa) for the greyish sandstone and the lowest (8 MPa) for the white sandstone sample, also associated with the lowest (Al+Fe)/Si value of 0.082. The humidity test showed that the 6 % water absorption was lower than the recommended ASTM value of 8 %. The sandstone samples were also subjected to various high temperatures to simulate possible fire conditions and it was found that the non alteration of the mineral species might be one of the reasons why the sandstones are regarded as the most refractory amongst the building materials typically used. Mossbauer spectroscopy revealed that iron is present in all the sandstones, mainly as Fe3 + with the black sandstone showing an additional presence of 3 % Fe2 + indicating that a higher iron content coupled to higher silicon content, contributes to an increase in the uniaxial compressive strength.

ON THE HISTORY AND MATHEMATICS OF THE EQUIVALENCE THEOREM

Trevor wrote three major histories, [62; 63; 64], as well as many mathematical papers in his multi-faceted career and it is a great pleasure for me to dedicate to his memory this oifering on the history and mathematics of the Schröder-Bernstein Theorem, intending that it reflect in a way he might have appreciated those two strands of his scholarly work. The historical material for my essay is gathered from a great variety of published sources and is no doubt known to specialists and to historians of Set Theory, but there is ample evidence that it is not widely known among other mathematicians, many of whom, like myself, use this theorem in their work and routinely present proofs of it to their undergraduate students. It is to these mathematicians that the essay is principally addressed.

On The History and Mathematics of The Equivalence Theorem

Trevor wrote three major histories, [62; 63; 64], as well as many mathematical papers in his multi-faceted career and it is a great pleasure for me to dedicate to his memory this offering on the history and mathematics of the Schroder-Bernstein Theorem, intending that it reflect in a way he might have appreciated those two strands of his scholarly work. The historical material for my essay is gathered from a great variety of published sources and is no doubt known to specialists and to historians of Set Theory, but there is ample evidence that it is not widely known among other mathematicians, many of whom, like myself, use this theorem in their work and routinely present proofs of it to their undergraduate students. It is to these mathematicians that the essay is principally addressed.