In the paper a **non**-**classical** type Cauchy problem is substantiated for a pseudoparabolic equation with **non**-smooth coefficients and with a fifth order dominating derivative. Classic Cauchy conditions are reduced to **non**-classic Cauchy conditions by means of integral representations. Such statement of the Cauchy problem has several advantages:

1. The intended natural numbers don’t need to be infinite. Despite being a sui generis claim (to say the least!), we think we can reasonably argue for this. Throughout the text we have argued that, from a moderate realist perspective, the constraints imposed on the class of intended models should be determined by actual number theoretic practice. In this sense, let us imagine two different counting practices: person A starts to count from 0, adds 1, then 2, 3, and so on – A will not have any greatest number where the counting stops; in fact, if we stepped into a time machine and went to the future an arbitrarily large numbers of years from now, in principle, we would discover that A hasn’t stop counting. Now, B will start very much like A: B starts with 0 then, 1, 2, 3, ... – however, for B there will be a certain greatest number n where she will stop the counting. For sake of argument ‘Let us, henceforth, fix n as some in- credibly large number, say, a number larger than the number of combinations of fundamental particles in the cosmos, larger than any number that could be sensible specified in a lifetime, so large that it has no physical meaning or psy- chological reality.’ (Priest 1994a : 338) As a consequence, we are not to expect that even with 100 life-times B can reach this magic number n. We have now the following question: is it the case that we actually count like A; or is it the case that we actually count more like B ? Prima facie, we would say that we count like A. The important thing to note is that in actual situations A and B seem to be counting according with the same rule. Recall that n is a number so great that is humanly impossible to reach (or even imagine). So, what makes us say that we count more like A is only the intuitions that we have about our counting practices in mere hypothetical (i.e. **non**-actual!) scenarios like those about reaching and counting after n; however our intuitions about what we would do or can do in hypothetical (**non**-actual) situations can be incredibly vague and unreliable and, more importantly, as Kripkenstein’s ‘quus’ function has shown us 1 , any rule-following ascriptions which are based in intuitions re-

105 Read more

monocytes have been found to produce large amounts of TNF 5 but are not able to differen- tiate into osteoclasts, 6 whereas **classical** mono- cytes (CD14+CD16 − ) are mainly producers of interleukin-10 6 and are able to differenti- ate into osteoclasts. 6 Differential therapeutic regulation of these monocyte subsets may explain the bone-sparing effect of TNF inhibi- tors. This has yet not been elucidated ex vivo.

This approach was originally outlined by Kerckhoff in [13]. For **classical** i.e.m.’s, he showed uniform distortion and consequently normality and unique ergodicity. However, for complete train tracks, there are two issues in making this work. Firstly, the probability of a particular split is the ratio of the volume of the part of the configuration space that is inside the smaller simplex picked out by the split to the volume of the entire configuration space. As we shall see in Chapter 5, this ratio can be very different from the proportion of the volumes of the ambient simplices. Secondly, splitting sequences of complete train tracks can have isolated blocks. These issues leave the proof of unique ergodicity for measured foliations in [13] incomplete.

91 Read more

In some instances, it was the presence of an organic agent within the reactive solution that disturbed the environment for **classical** nucleation and free growth. Instead, the aggregation of precursor ions was enhanced, leading to the formation of disordered particles, typically consisting of many nanocrystallites embedded in an organic matrix. These particles would then undergo a recrystallization process, eventually leading to single crystals. In the case of the decorated ZnO microstadiums, a hydrothermal method was reported where many nanocones of ZnO could be grown on the inner and outer columnar surfaces of ZnO microstadium walls. It had previously been unclear why the additional growth occurred in this way as it would be more energetically favourable to simply extend the existing crystal structure (through **classical** growth) rather than to form the cones or branches on the surface. Through studying the nanocone growth after just 10 min of hydrothermal treatment time it was revealed that the organic component used in the synthetic solution, 1,3-propanediamine, had enhanced the aggregation of precursor ions on the microstadium surfaces as they were attracted by the lone electron pairs on the O and N atoms on the amine molecules. These aggregates then recrystallised to form many well aligned, sharp-tipped ZnO nanorods.

138 Read more

By applying the approximation and splitting rules to the nodes of the upper part, we can always obtain a transformation in which the “lower part is in display”. Namely, all the subformulas whose main node does not belong anymore to the upper part, which is shaded in the picture, and which contain critical occurrences of proposition variables, occur now as the main formulas either on the left or on the right of inequalities, i.e. they occur “in display”. The syntactic restrictions on induc- tive and Sahlqvist inequalities guarantee that if such a formula is in display on the left (resp. right), then it is a left (resp. right) adjoint or a left (resp. right) residual in the critical coordinate; hence, by applying the appropriate adjunction or residuation rules, the given inequality can be equivalently rewritten in such a way that the critical occurrence is now in display, either on the left or on the right. This provides us with a “minimal valuation”, namely with inequalities of the form α ≤ p if the order-type of p is 1, and of the form p ≤ α if the order-type of p is ∂. The **non**-critical occurrences of the proposition variable p will have the appropriate polarity to receive the minimal valuation, hence inductive and Sahlqvist inequalities make sure that the Ackermann rule can always be applied. Finally, referring back to the discussion in Chapter 3, we noticed that the compositional struc- ture of Sahlqvist formulas guarantees that at least one of the two routes which constitutes the core of the J´ onsson-style strategy. Here, the same order-theoretic properties guarantee that the decompositional strategy of the ALBA is always successful. In Chapter 7, we will continue this discussion.

82 Read more

[4] Pedro, A. F. C., Torres, D. F. M. & Zinober, A. S. I. (2010). “A **Non** **Classical** Class of Variational Problems with Application in Economics” in International Journal of Mathematical Modeling and Numerical Optimization, Vol. 1. No. 3. pp. 227-236.

We propose a subsampling method for robust estimation of regression models which is built on **classical** methods such as the least squares method. It makes use of the **non**-robust nature of the underlying **classical** method to find a good sample from regression data contaminated with outliers, and then applies the **classical** method to the good sample to produce robust estimates of the regression model parameters. The subsampling method is a computational method rooted in the bootstrap methodology which trades analytical treatment for intensive computation; it finds the good sam- ple through repeated fitting of the regression model to many random subsamples of the contaminated data instead of through an analytical treatment of the outliers. The subsampling method can be applied to all regression models for which **non**-robust **classical** methods are available. In the present paper, we focus on the basic formulation and robust- ness property of the subsampling method that are valid for all regression models. We also discuss variations of the method and apply it to three examples involving three different regression models.

16 Read more

for a state ρ defined by the statistical operator a (i.e., a is a self-adjoint operator on H with **non**-negative spectrum and trace(a) = 1). The above identity reveals that con- ditionalization becomes identical with the state transi- tion of the L¨ uders - von Neumann measurement process. Therefore, the conditional probabilities defined in section III can be regarded as a generalized mathematical model of projective quantum measurement.

My claim that there is no central notion to the theory of meaning of the kind that Dummett envisages, or more loosely, meaning need not be analyzed in terms of **classical** or **non**-**classical** truth-conditions, amounts to a proposal for reidentifying realism and anti-realism. Up until now I have followed Dummett in identifying realism about sentences of a disputed class with the thesis that the meaning of the sentences should be analyzed in terms of the notions of truth and fa ls ity which obey the principle of bivalence and in identifying anti-realism with a denial of this thesis. While I s t ill believe that an acceptance of bivalence for sentences of a disputed class is characteristic of a local anti-realism and a rejection of bivalence for the sentences is characteristic of the corresponding local anti-real ism,I believe that the notion of meaning is irrelevant to the characterizations of these positions. To mimic the f ir s t passage quoted from Dummett in this chapter: a local realism is correctly identified with the thesis that the conditions for the truth of the disputed sentences consist in objective states of affairs which obtain or fa il to obtain, regardless of the evidencewe possess for them and a local anti-realism is correctly identified with the thesis that the conditions for the truth of the disputed sentences consist in our capacity to possess evidence for the sentences.

157 Read more

One or more of a variety of immunological, morphological, or symptomatic manifestations that are precipitated by the ingestion of gluten in individuals in whom CD has been excluded—**Non**-coeliac gluten sensitivity (NCGS) is a condition in which gluten ingestion leads to morphological or symptomatic manifestations despite the absence of CD. 172–176 As opposed to CD, NCGS may show signs of an activated innate immune response but without the enteropathy, elevations in tTG, EMA or DGP antibodies, and increased mucosal permeability characteristic of CD. 173 Recently, Biesiekierski et al in a double-blind randomized trial showed that patients with NCGS truly develop symptoms when eating gluten. 156 It is unclear at this time what components of grains trigger symptoms in individuals with NCGS and whether some populations of NCGS patients have subtle small intestinal morphological changes. While there currently is no standard diagnostic approach to NCGS, systematic evaluation should be conducted including exclusion of CD and other inflammatory disorders.

25 Read more

a and the point is not moving uniformly and is not at rest toward K´. The main conclusion that can be drawn is that all frames of reference, which are not moving uniformly or are not at rest toward particular frame of reference, are **non**-inertial. Or in **non**-inertial frames of reference alterations are necessary to be done in all kinematics values and laws deduced for inertial frames of reference.

The concepts of “mentality and” identity “, in our opinion, reveal the peculiarity of memory studies in the framework of cultural studies and the paradigmatic shift that occurred in knowledge of the past in the twentieth century. This explains why the idea of identity in modern science originates from the study of the consciousness of the patriarchal collective. Identification in this case becomes self-identification with the collective in a spontaneously direct form. As contrasted with the representatives of German **classical** philosophy, whose act of rational self-consciousness is the basis of the universe, modern ideas about identity are a return to what seemed to be left in the distant past. Through a sense of collective involvement we return from conscious personal choice to the mechanisms of unconscious rallying. As M. Halbwachs and J. Assmann show, they are modified at the level of religious consciousness. And in modern society an irrationally organized cultural memory comes to the fore. First and foremost, it is due to the fact that an irrational collective identity, unlike individual self-consciousness, is an effective form of manipulation. The mechanisms of the formation of the “mythology from above” are innovation of the era of managed democracy.

In India, along with the indigenous Ayurvedic system of medicine other alternative systems of medicine like Siddha and Unani are in practice since a prehistoric period. Although there is a similarity between the basic principle of treatment in these three systems of medicine, there are differences in formulations and method of standardization. The modern Ayurvedic formulations include tablets, capsules, syrups, solutions. Similarly, most of the Siddha formulations utilize mineral and metal in the formulations. These formulations are categorized into Uppu, Pashanam, Uparasam, Ratnas and Uparatnas, Loham, Gandhakam. Siddha system of medicine also includes drugs of animal and plant origin having a similar profile as that of Ayurvedic drugs. However, standards pertaining to the limit of impurities, heavy metals, and toxins in modern Siddha formulations are not defined in the Siddha Pharmacopeia of India. Hence, the standardization of Siddha formulations becomes a challenge. Due to the proximity of a few Siddha drugs with Ayurvedic preparations, the earlier can be standardized in a similar fashion as that of the later preparations. Unani system of medicine got introduced into India during 1350 AD. Since then this system of medicine has undergone many folds of development and modernization. The Government of India, Ministry of AYUSH has developed the Unani Pharmacopeia of India. This official monograph constitutes 50 **classical** Unani formulations and their standardization techniques, and limits of heavy metal content are also mentioned. However, the modern aspects of good manufacturing practice for herbal drugs were not addressed sufficiently in the published monographs.

The second issue addressed here deals with the effect of local geology. In the NEHRP guidelines, the local geology is quantified by the shear wave velocity of the local soil [9]. Since this data is included in the population of earthquake records used here, it is simple to determine any correlation. Again, the peak displacements for a range of frictions were determined and these results were compared with the shear wave velocity. As seen in figure 4.4, there is no discernable correlation between the two variables when using a **classical** coefficient of friction of 0.1. Similar results were also calculated for **classical** frictions of 0.2, 0.3, 0.4 and 0.5. So there is again no need to incorporate this variable into a design/analysis methodology. But, this may not be the case for regions of high shear wave velocity (>750 m/s) or very low velocity (<200 m/s) which are outside of the range of earthquakes used here. This particularly applies to areas seated on rock or weathered rock which are a concern for nuclear facilities located on the east coast of the United States of America.

232 Read more

p-values of 1% and 10%. We see for example that after 350000 runs, we have more than 50% chance of being able to rule out **classical** states with a confidence of 1 − = 99%. For n = 12500, we find hNi ' 402964 for a confidence of 99%. Note that to perform 403000 runs with a repetition rate of 1Hz takes about 112 hours. The latter provides an upper bound on the timescale of the proposed experiment to get a p-value of 1%. A similar analysis for a p-value of 10% shows that 46 hours are likely to be enough to detect the **non**- **classical** nature of a single photon superposed with vacuum using the human eye. This goes down to 35 hours when considering a threshold at 3 photons while keeping 8% efficiency and to 29 hours for an efficiency of 10% and a threshold at 7 photons.

There are good reasons for the nonclassicist to start by seeking to generalize the **classical** theory of mind, leaving consideration of other classically based theories (whether in chemistry, geography, ecology or even philosophy) for later. The first reason for this is that every **non**- classicism undercuts the **classical** theory of mind, whereas it does not automatically undercut a classically-based theory of ecology. The core principles of the theory of mind themselves concern truth and logic explicitly (as the aim of belief, or norm of coherence), so revisions to our account of the latter have an immediate impact on our account of the former. A theory of ecology, by contrast, needn’t mention truth-statuses at all, and draws on logic only implicitly, when we derive consequences of its principles. Logical or semantic revisionism may undercut a classically-based ecology, but equally it may turn out to leave it untouched: that (LEM) fails to be a logical truth does not mean that the law of excluded middle has exceptions expressible in the language of ecological theory; and an invalid argument form may preserve truth in all ecological applications. 5

36 Read more

Besides modal and intuitionistic logics there are many other important **non**- **classical** logics. One example of such logics are **non**-monotonic logics which be- came an important new research field in logic after a seminal issue of the Artificial Intelligence journal in 1980. In one of these papers, Raymond Reiter defined what is now called Reiter’s default logic [97], which is still one of the most popular sys- tems under investigation in this branch of logic. 11 In a nutshell, **non**-monotonic logics are a family of knowledge representation formalisms mostly targeted at modelling common-sense reasoning. Unlike in **classical** logic, the characteris- ing feature of such logics is that an increase in information may lead to the withdrawal of previously accepted information or may blocks previously possible inferences.

57 Read more

Macromolecular matrices play a key role in establishing the architectural complexity and mechanical properties of biominerals by directing the organization of the mineralized component. 1-3 The ability of the matrix to perform this function is determined by both its structural relationship with the incipient nucleus 4 and the changes to the energy landscape it imposes upon the mineralizing constituents. 5 A number of studies have explored the structural aspect, 1-4,6,7 but little is known about the energetic controls. Moreover, the recent discovery that calcium carbonate 8 and phosphate 4 solutions contain clusters prior to nucleation Ñ i.e., pre- nucleation clusters Ñ that seem to be stable relative to the free ions 8 combined with observations of **non**-equilibrium amorphous precursors in numerous biomineral 1,9,10 and biomimetic systems, 4,11,12 raises the question of whether the **classical** description 5 of nucleation dynamics is applicable to matrix-directed mineralization. This same question arises when considering mineral nucleation in geochemical settings where a surrounding mineral matrix, which is often coated with biofilms or other organic layers, is likely to influence nucleation kinetics. While these issues are difficult to address in the context of three-dimensional biological matrices or geological reservoirs, self-assembled monolayers (SAMs) of organothiols on noble metal surfaces, which can template mineral nucleation on distinct crystallographic planes with a high degree of specificity, offer an excellent 2D model. 12-16

38 Read more

principle of complementarity, have quantum probability more or less forced upon them. Here my goal has been somewhat different: to investigate the role of quantum probability in modelling the "complementarity" behaviour exhibited by quantum systems. It has been demonstrated that (i) complementary properties are incorporated into quantum probability via the modified contradictory inference, based on the static formulation of conditional probability (§1.3); and that (ii) incompatible observables can be completely characterised by a quantitative measure of incompatibility, based on **non**-**classical** features of quantum probability (§1.4). I should emphasise that these results are not intended to support either the principle of complementarity or quantum probability as "explanations" of quantum phenomena, but rather to indicate the close connections between them as

153 Read more