Quotients, exactness, and nuclearity in the operator system category

We continue our study of tensor products in the operator system category. We define operator system quotients and exactness in this setting and refine the notion of nuclearity by studying operator systems that preserve various pairs of tensor products. One of our main goals is to relate these refinements of nuclearity to the Kirchberg conjecture. In particular, we prove that the Kirchberg conjecture is equivalent to the statement that every operator system that is (min,er)-nuclear is also (el,c)-nuclear. We show that operator system quotients are not always equal to the corresponding operator space quotients and then study exactness of various operator system tensor products for the operator system quotient. We prove that an operator system is exact for the min tensor product if and only if it is (min,el)-nuclear. We give many characterizations of operator systems that are (min,er)-nuclear, (el,c)-nuclear, (min,el)-nuclear and (el,max)-nuclear. These characterizations involve operator system analogues of various properties from the theory of C*-algebras and operator spaces, including the WEP and LLP.

Distinguished algebraic semantics for t-norm based fuzzy logics:Methods and algebraic equivalencies

This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and ?-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics-namely the class of algebras defined over the real unit interval, the rational unit interval, the hyperreals (all ultrapowers of the real unit interval), the strict hyperreals (only ultrapowers giving a proper extension of the real unit interval) and finite chains, respectively-and we survey the known completeness methods and results for prominent logics. We also obtain new interesting relations between the real, rational and (strict) hyperreal semantics, and good characterizations for the completeness with respect to the semantics of finite chains. Finally, all completeness properties and distinguished semantics are also considered for the first-order versions of the logics where a number of new results are proved. © 2009 Elsevier B.V. All rights reserved.

The C*-algebra of ax+b-like groups

We describe the C*-algebras of " ax+b" -like groups in terms of algebras of operator fields defined over their dual spaces.

Hydrogel-Forming Microneedles Increase in Volume During Swelling in Skin, but Skin Barrier Function Recovery is Unaffected

We describe, for the first time, quantification of in-skin swelling and fluid uptake by hydrogel-forming microneedle (MN) arrays and skin barrier recovery in human volunteers. Such MN arrays, prepared from aqueous blends of hydrolyzed poly(methylvinylether/maleic anhydride) (15%, w/w) and the cross-linker poly(ethyleneglycol) 10,000 Da (7.5%, w/w), were inserted into the skin of human volunteers (n = 15) to depths of approximately 300 μm by gentle hand pressure. The MN arrays swelled in skin, taking up skin interstitial fluid, such that their mass had increased by approximately 30% after 6 h in skin. Importantly, however, skin barrier function recovered within 24 h after MN removal, regardless of how long the MN had been in skin or how much their volume had increased with swelling. Further research on closure of MN-induced micropores is required because transepidermal water loss measurements suggested micropore closure, whereas optical coherence tomography indicated that MN-induced micropores had not closed over, even 24 h after MN had been removed. There were no complaints of skin reactions, adverse events, or strong views against MN use by any of the volunteers. Only some minor erythema was noted after patch removal, although this always resolved within 48 h, and no adverse events were present on follow-up.

Characterisations of the weak expectation property

We use representations of operator systems as quotients to deduce various characterisations of the weak expectation property (WEP) for C∗ -algebras. By Kirchberg’s work on WEP, these results give new formulations of Connes’ embedding problem.

The solvable Lie group N_{6, 28}: an example of an almost C_0(\mathcal{K})-C*-algebra

Motivated by the description of the C*-algebra of the affine automorphism group N6,28 of the Siegel upper half-plane of degree 2 as an algebra of operator fields defined over the unitary dual View the MathML source of the group, we introduce a family of C*-algebras, which we call almost C0(K), and we show that the C*-algebra of the group N6,28 belongs to this class.

Quantum Chromatic Numbers via Operator Systems

We define several new types of quantum chromatic numbers of a graph and characterize them in terms of operator system tensor products. We establish inequalities between these chromatic numbers and other parameters of graphs studied in the literature and exhibit a link between them and non-signalling correlation boxes.

Difficulties generating self-compassion: An interpretative phenomenological analysis

The aim of the present study was to make an idiographic investigation about the difficulties that are encountered by people who self-identify as having difficulties with self-compassion. Although a growing number of studies have been carried out concerning the concept of self-compassion, most research designs were quantitative. Based on this gap, the current study expanded the scope to include a qualitative dimension of the recent literature on self-compassion and Interpretative Phenomenological Analysis (IPA) was adopted as methodological preference, which particularly monitors the lived experience of participants. In consequence of four in-depth semi-structured interviews, four super-ordinate themes emerged; the double-edged-sword: perfectionism, the flaws of compassion, the effects of a third person, and the advantages of self-criticism. In line with pre-existing research, these findings explored the reasons behind self-undermining behaviours and misconstructions about self-compassion, which are a barrier to gentle self-talk. Furthermore, unfavourable effects of the social environment prime participants to maladaptive perfectionism and excessive self-criticism, which are considered a success formula by the participants. This study's purpose is to present a detailed roadmap about the self-destructive journey of the people with low self-compassion. It will help researchers and clinicians to develop future interventions in order to cultivate kind and encouraging attitudes in self-critical people.

Structural analysis of Turtle mountain (Alberta) using digital elevation model: Toward a progressive failure

In 1903, the eastern slope of Turtle Mountain (Alberta) was affected by a 30 M m3-rockslide named Frank Slide that resulted in more than 70 casualties. Assuming that the main discontinuity sets, including bedding, control part of the slope morphology, the structural features of Turtle Mountain were investigated using a digital elevation model (DEM). Using new landscape analysis techniques, we have identified three main joint and fault sets. These results are in agreement with those sets identified through field observations. Landscape analysis techniques, using a DEM, confirm and refine the most recent geology model of the Frank Slide. The rockslide was initiated along bedding and a fault at the base of the slope and propagated up slope by a regressive process following a surface composed of pre-existing discontinuities. The DEM analysis also permits the identification of important geological structures along the 1903 slide scar. Based on the so called Sloping Local Base Level (SLBL) an estimation was made of the present unstable volumes in the main scar delimited by the cracks, and around the south area of the scar (South Peak). The SLBL is a method permitting a geometric interpretation of the failure surface based on a DEM. Finally we propose a failure mechanism permitting the progressive failure of the rock mass that considers gentle dipping wedges (30°). The prisms or wedges defined by two discontinuity sets permit the creation of a failure surface by progressive failure. Such structures are more commonly observed in recent rockslides. This method is efficient and is recommended as a preliminary analysis prior to field investigation.

Investigations into the extraction and the determination of polycyclic aromatic hydrocarbons (PAHs) from water by solid-phase extraction and capillary gas chromatography/ mass spectrometry

Factors affecting the detennination of PAHs by capillary GC/MS were studied. The effect of the initial column temperature and the injection solvent on the peak areas and heights of sixteen PAHs, considered as priority pollutants, USillg crosslinked methyl silicone (DB!) and 5% diphenyl, 94% dimethyl, 1% vinyl polysiloxane (DBS) columns was examined. The possibility of using high boiling point alcohols especially butanol, pentanol, cyclopentanol, and hexanol as injection solvents was investigated. Studies were carried out to optimize the initial column temperature for each of the alcohols. It was found that the optimum initial column temperature is dependent on the solvent employed. The peak areas and heights of the PAHs are enhanced when the initial column temperature is 10-20 c above the boiling point of the solvent using DB5 column, and the same or 10 C above the boiling point of the solvent using DB1 column. Comparing the peak signals of the PAHs using the alcohols, p-xylene, n-octane, and nonane as injection solvents, hexanol gave the greatest peak areas and heights of the PAHs particularly the late-eluted peaks. The detection limits were at low pg levels, ranging from 6.0 pg for fluorene t9 83.6 pg for benzo(a)pyrene. The effect of the initial column temperature on the peak shape and the separation efficiency of the PARs was also studied using DB1 and DB5 columns. Fronting or splitting of the peaks was obseIVed at very low initial column temperature. When high initial column temperature was used, tailing of the peaks appeared. Great difference between DB! and.DB5 columns in the range of the initial column temperature in which symmetrical.peaks of PAHs can be obtained is observed. Wider ranges were shown using DB5 column. Resolution of the closely-eluted PAHs was also affected by the initial column temperature depending on the stationary phase employed. In the case of DB5, only the earlyeluted PAHs were affected; whereas, with DB1, all PAHs were affected. An analytical procedure utilizing solid phase extraction with bonded phase silica (C8) cartridges combined with GC/MS was developed to analyze PAHs in water as an alternative method to those based on the extraction with organic solvent. This simple procedure involved passing a 50 ml of spiked water sample through C8 bonded phase silica cartridges at 10 ml/min, dried by passing a gentle flow of nitrogen at 20 ml/min for 30 sec, and eluting the trapped PAHs with 500 Jll of p-xylene at 0.3 ml/min. The recoveries of PAHs were greater than 80%, with less than 10% relative standard deviations of nine determinations. No major contaminants were present that could interfere with the recognition of PAHs. It was also found that these bonded phase silica cartridges can be re-used for the extraction of PAHs from water.

ReAlM - a system to manipulate relations

Given a heterogeneous relation algebra R, it is well known that the algebra of matrices with coefficient from R is relation algebra with relational sums that is not necessarily finite. When a relational product exists or the point axiom is given, we can represent the relation algebra by concrete binary relations between sets, which means the algebra may be seen as an algebra of Boolean matrices. However, it is not possible to represent every relation algebra. It is well known that the smallest relation algebra that is not representable has only 16 elements. Such an algebra can not be put in a Boolean matrix form.[15] In [15, 16] it was shown that every relation algebra R with relational sums and sub-objects is equivalent to an algebra of matrices over a suitable basis. This basis is given by the integral objects of R, and is, compared to R, much smaller. Aim of my thesis is to develop a system called ReAlM - Relation Algebra Manipulator - that is capable of visualizing computations in arbitrary relation algebras using the matrix approach.

Extending relAPS to first order logic

RelAPS is an interactive system assisting in proving relation-algebraic theorems. The aim of the system is to provide an environment where a user can perform a relation-algebraic proof similar to doing it using pencil and paper. The previous version of RelAPS accepts only Horn-formulas. To extend the system to first order logic, we have defined and implemented a new language based on theory of allegories as well as a new calculus. The language has two different kinds of terms; object terms and relational terms, where object terms are built from object constant symbols and object variables, and relational terms from typed relational constant symbols, typed relational variables, typed operation symbols and the regular operations available in any allegory. The calculus is a mixture of natural deduction and the sequent calculus. It is formulated in a sequent style but with exactly one formula on the right-hand side. We have shown soundness and completeness of this new logic which verifies that the underlying proof system of RelAPS is working correctly.

RelMDD-A Library for Manipulating Relations Based on MDDs

Relation algebras is one of the state-of-the-art means used by mathematicians and computer scientists for solving very complex problems. As a result, a computer algebra system for relation algebras called RelView has been developed at Kiel University. RelView works within the standard model of relation algebras. On the other hand, relation algebras do have other models which may have different properties. For example, in the standard model we always have L;L=L (the composition of two (heterogeneous) universal relations yields a universal relation). This is not true in some non-standard models. Therefore, any example in RelView will always satisfy this property even though it is not true in general. On the other hand, it has been shown that every relation algebra with relational sums and subobjects can be seen as matrix algebra similar to the correspondence of binary relations between sets and Boolean matrices. The aim of my research is to develop a new system that works with both standard and non-standard models for arbitrary relations using multiple-valued decision diagrams (MDDs). This system will implement relations as matrix algebras. The proposed structure is a library written in C which can be imported by other languages such as Java or Haskell.

Charles Larned letter, April 3, 1813.

Charles Larned (1791-1834) was a lawyer and American military officer who served during the War of 1812. He was the son of Simon Larned (1753-1817), who served as a captain in the Revolutionary War and was a member of the United States Congress from Massachusetts from 1804-1805. Charles studied law in the office of Henry Clay in Kentucky, and was dining with a group of prominent citizens when word was received that General William Henry Harrison could soon be overpowered by General Henry Proctor. Colonel Owen, a member of the group, organized a regiment to reinforce Harrison’s troops. Larned became a member and subsequently survived the River Raisin Massacre and was later present at the Battle of the Thames. He was also part of a group of men who learned of General William Hull’s plan to surrender Detroit to the British and planned to overtake him should this occur. However, the plan failed, Hull did surrender and the men became prisoners of the British. After the war, Larned became a lawyer, and served as Attorney General of Michigan Territory during the Black Hawk War. During the cholera epidemic of 1834, he worked tirelessly to assist others, but was stricken with the disease and died. Letter Transcription: Pittsfield, April 8, 1813 I think that by this time my dear Charles you will allow I have some reason to give you a gentle reprimand for breach of duty—but I will not censure you upon suspicion maybe you have substantial reasons—at any rate one cannot very graciously reproach the other for negligence I for one am healthy as ham & that we have so seldom exchanged letters during your absence & on my honor promise to be a better girl in future—but the truth is my Dear Charles I am secretary for the Family—Mama you know never writes & James but seldom & they are all dispersed in different directions, consequently I have many calls upon my time—this to be sure is a pleasant duty & I urge it only as a slight palliation for my remissness if you should consider it as such—now I have finished my preface—I will try to be more interesting & doubtless I succeed. Our dear Father we hope & trust is now in Green Bush, where he will probably remain a month perhaps & from thence he expects to go to Sacket’s harbor—at which place you know our troops are fast collecting-- We shall hope to see him either here or there before he goes. Brother George I believe is [still] at Plattsburgh but expects soon to be removed to some other military part perhaps with Papa (I hope so at least). We have just got letters from Brothers Sylvester & Joseph at Middlebury—they are in good health. Mama has for some weeks been afflicted with an inflammation in her eyes but seems now to be convalescing. Sister Martha has been somewhat unwell for a few weeks but is now tolerably recovered. James & myself are both in our usual good health & at this time seated by the same stand, one reading, the other writing. Thus my Dear Charles have I given you an abstract history of our Family—but here indeed is a wonderful omission; not a word about Miss Harriet Hunt, who in truth ought to have been noted first but the last she’s not the least in my memory. She is much grown since you saw her, but does not speak as fluently as we could wish—a few word she can say. Probably before this you have been informed of the great loss your friend Sherrill has sustained in the death of his mother—also of the revolution that has taken place in Hackbridge as it respects the religion & morality of the place that more than one hundred on the plain have become religious converts & c—indeed I am at a loss what to say that will afford your pleasure—a narrative at this time must be gloomy indeed. The distressing situation of our country at this time would make almost any recital melancholy. The prevailing epidemic has swept off many of your acquaintance no doubt. Mrs. Dewey of Williamstown, the sister of Mrs. Danforth, has left a Husband, Children & many Friends sincerely to lament her loss—some few have died in our village, but we have escaped astonishingly –it has raged in every town about us--If we are unwilling to acknowledge a God in his mercies. I fear she shall be compelled to do it in the awfulness of his judgments.--------I am much [pleased] with our new neighbors the Parsons Wife & a Miss Woodward her cousin is a fine girl, I think, Mrs. Allen has not a handsome face but something in her manner that interests one her person I think the handsomest I ever saw & the Parson seems well pleased with his selection—Mrs. Ripley is with them this winter & will probably remain thro the summer—Her husband at [Sackett’s Harbor] little or no alteration is apparent since her marriage—she seems as gay & fond of company as ever.-------Mrs. [McKnight] it is expected will commence housekeeping in about three weeks in the house formerly occupied by Mr…. [Report] says that Mr. Goodman & Clarissa Weller are soon to be married & many other things that I must omit to mention for Mama wants a… PS reserved--now my Dear Charles remember you are considerably… & I am confident you have as much leisure as I have –… be ceremonious but write whenever I find time not & I beg… the same – I tell James I shall not send his love for he must write himself. I shall anxiously expect you to write & do not disappoint your affectionate, sister--H One word my Dear Charles from your affectionate Mother who longs to see Her Dear son Charles—but being deprived of that rich blessing at present—begs Him so to conduct that she may hope for it ere long—do you search the Scriptures and keep the Sabbath holy unto the Lord—and all the sacred Commandments of God—it is my ardent desire…He would protect, support and provide for your soul and body and believe me your affectionate friend and Mother. R Larned.

Region Connection Calculus: Composition Tables and Constraint Satisfaction Problems

Qualitative spatial reasoning (QSR) is an important field of AI that deals with qualitative aspects of spatial entities. Regions and their relationships are described in qualitative terms instead of numerical values. This approach models human based reasoning about such entities closer than other approaches. Any relationships between regions that we encounter in our daily life situations are normally formulated in natural language. For example, one can outline one's room plan to an expert by indicating which rooms should be connected to each other. Mereotopology as an area of QSR combines mereology, topology and algebraic methods. As mereotopology plays an important role in region based theories of space, our focus is on one of the most widely referenced formalisms for QSR, the region connection calculus (RCC). RCC is a first order theory based on a primitive connectedness relation, which is a binary symmetric relation satisfying some additional properties. By using this relation we can define a set of basic binary relations which have the property of being jointly exhaustive and pairwise disjoint (JEPD), which means that between any two spatial entities exactly one of the basic relations hold. Basic reasoning can now be done by using the composition operation on relations whose results are stored in a composition table. Relation algebras (RAs) have become a main entity for spatial reasoning in the area of QSR. These algebras are based on equational reasoning which can be used to derive further relations between regions in a certain situation. Any of those algebras describe the relation between regions up to a certain degree of detail. In this thesis we will use the method of splitting atoms in a RA in order to reproduce known algebras such as RCC15 and RCC25 systematically and to generate new algebras, and hence a more detailed description of regions, beyond RCC25.