bluuebunny/crossref_metadata_2025_split huggingface dataset:
Extensions to the PMP
Authors: Hocking Leslie M 
Published: November 2023

Abstract
The basic form of the PMP can be extended to apply to more general targets than the single point so far assumed. We can also include the effect ofa terminal cost, and we can make a simple amendment of the principle to allow non-autonomous problems to be treated. It often happens that we do not need to specify the final state of the system completely. It may be sufficient, for example, that one component only of the state vector must reach a specified value, while the other components are free to take any values consistent with the solution of the state equations. In that case, we lose information about the solution of the state equations, and this lack must be supplied from another source. If not, we would end with an undetermined problem. The extra conditions come from a constraint on the co-state vector at the terminal time. These conditions are stated and applied here, but, in accordance with our procedure, the reason for their validity is postponed until Chapter 9, where we give an outline proof of the PMP and its extensions.
Introduction and an example
Authors: Pretzel Oliver 
Published: November 2023

Abstract
Before attempting to construct an example of a finite field, we should discuss why there is any need for fields other than the binary field B. After all, practically all computation is done in binary. So why make life harder by working over other fields? There are, however, several good reasons why a knowledge of finite fields is indispensable in the study of error-correcting codes, and I shall list three of the more obvious ones here.
The structure of finite fields
Authors: Pretzel Oliver 
Published: November 2023

Abstract
Now that you have seen a method of constructing finite fields, we turn to the task of analysing their structure. In this chapter we establish four fundamental results. These results are all related to a prime number, called the characteristic of the field, that determines its arithmetical properties. As the results are analytical in nature, their proofs are not applied directly, like the proofs involving Euclid’s algorithm. Rather, the characteristic is implicitly used by many algorithms. You can use the algorithms without understanding the theory, but you will not be able to design or modify them.
Primitive elements
Authors: Pretzel Oliver 
Published: November 2023

Abstract
You will recall that in our example of GF(16) we introduced ‘logarithms’ for non-zero field elements that could be used like conventional logarithms to convert multiplication into addition. This is certainly of practical significance, since addition modulo 15 is easily implemented on a chip, while polynomial multiplication followed by division with remainder (the method used to define multiplication) is both more complicated and slower. On the other hand, the existence of such logarithms is closely linked to a remarkable property possessed by finite fields that is of great theoretical importance. If logarithms exist, then every non-zero element of the field is an integer power of the element with a logarithm 1. In the case of GF(16) every non-zero element is a power of the element we have denoted by 2.
BCH codes as subcodes of Hamming codes
Authors: Pretzel Oliver 
Published: November 2023

Abstract
How do you modify a Hamming code to correct two errors? In other words, how can you increase its minimum distance from 3 to 5? You will either have to lengthen the code words or eliminate some of them from your code. Correcting two errors in a long word may not be much better than correcting one error in a short one. So we adopt the second approach. That is, we shall try to produce a double error-correcting subcode of the Hamming code by removing some code words to make the new code sparser.
Movements of the hyperbolic plane
Authors: Hemion Geoffrey 
Published: November 2023

Abstract
The hyperbolic plane H is the universal covering space of any compact surface S whose Euler characteristic is less than zero. Let f : S → S be a homeomorphism of the surface onto itself. Then there is a mapping f*: H → H which is a ‘lifting’ off to the covering space. More specifically, the projection of H onto S is a mapping p : H → S. (It maps each copy of the fundamental region in H onto the single fundamental region of S.) Then the lifted mapping f* has the property that for each point x ϵ H we have f(p(x)) = p(f*(x)).
Matrix Eigenvalue Problems
Authors: Kockler Norbert 
Published: November 2023

Abstract
Characteristic properties of natural systems can often be described by eigenvalues of certain differential equations, see Chapter 8. If the differential equation is discretized, a matrix eigenvalue problem has to be solved. This kind of problem will be considered in this chapter. We will restrict ourselves to real matrices. But the eigenvalues of a real matrix may be complex numbers.
Boundary Value and Eigenvalue Problems for Ordinary Differential Equations
Authors: Kockler Norbert 
Published: November 2023

Abstract
The mathematical theory for (two-point) boundary and eigenvalue problems for ordinary differential equations (ODEs) is not as standardized as that for initial value problems. But that does not mean that these problems do not play an important role for a lot of engineering and other applications. There are some problems of practical importance, where the mathematician cannot determine the question of existence or uniqueness of solutions, but they are regularly solved approximately with numerical methods.
Partial Differential Equations
Authors: Kockler Norbert 
Published: November 2023

Abstract
Partial differential equations (PDEs) are one of the most important subjects of applied mathematics, with innumerable applications in science and engineering. Accordingly numerical methods for their approximate solution are of some importance. In spite of these facts this chapter is short, because the field of partial differential equations is too large to be considered in detail within a general text on numerical methods like this one.
More About Paley-Wiener Spaces
Authors: Higgins J R 
Published: November 2023

Abstract
The four topics covered in this chapter are not directly concerned with sampling, but with various aspects of Paley-Wiener spaces. Since these spaces are typically collections of band-limited functions, and the notion of band-limitation in one form or another runs through all our work on sampling, this material has been included to provide some necessary background, and to lend perspective on these important spaces.For general reference it will be convenient to have at our disposal a collection of Paley-Wiener theorems.
Errors And Aliasing
Authors: Higgins J R 
Published: November 2023

Abstract
The act of expanding a function into a sampling series is fraught with the possibility of incurring errors of various kinds. These are to be seen as deviations from the desired goal and usually arise from an incomplete knowledge of all the parameters; this is often due to our incapacity to measure with complete accuracy. Sometimes errors are incurred deliberately, especially if there is some trade-off value in doing so. Let us recall that we are always dealing with the case in which functions require infinitely many samples for exact reconstruction.Several different kinds of error have been identified, and they have been studied intensively over the past few decades. The main ones are as follows.The truncation error arises if one ignores all the samples outside a finite interval; it always occurs in practice of course. The object function cannot be reconstructed exactly because there is insufficient information. A more general kind of error occurs if samples are missing from some locations; it is called the information loss error.
Ordered sets, lattices, and universal algebra
Authors: Blyth T S , Varlet J C 
Published: November 2023

Abstract
It is of course impossible to give a full account of ordered sets, lattices, and universal algebra in a few pages, so we refer the reader to the various books cited in the bibliography. Nevertheless, in order to make this monograph reasonably selfcontained, we shall summarise in this introductory chapter the fundamental notions that we shall use throughout. More specific concepts that we shall require will be defined as necessary. As far as notation is concerned, we provide an index of the various symbols that are used throughout.
Congruence relations
Authors: Blyth T S , Varlet J C 
Published: November 2023

Abstract
Let (L;f) be an Ockham algebra. Then an Ockham algebra congrnence (or, briefly, a congrnence) on L is an equivalence relation that has the substitution property for both the lattice operations and for the unary operation f. It follows that every congruence is in particular a lattice congrnence and it is essential to distinguish these two types. In order to do so, we shall use the subscript ‘lat’ to denote a lattice congruence.
Duality theory
Authors: Blyth T S , Varlet J C 
Published: November 2023

Abstract
Duality theory in the context of distributive lattice-ordered algebras has rather a long history. It was in 1933 that G. Birkhoff established his famous representation theorem for finite distributive lattices and, about three years later, M. H. Stone developed a representation theory for arbitrary boolean algebras, using topological methods. In the early seventies, H. A. Priestley provided an ingenious common generalisation of both these theories, thus allowing questions of a lattice-theoretic nature ‘to be translated into the language of ordered topological spaces’ and usually be resolved more easily, the dual space generally being simpler and more tractable than the algebra itself. Of course, it is impossible to give here a complete survey of the theory of duality; for this we refer the reader to [78], [79], and [63]. Here we shall simply introduce the concepts and results that we shall require.
The lattice of subvarieties
Authors: Blyth T S , Varlet J C 
Published: November 2023

Abstract
A subclass of a variety V which is also a variety is called a subvariety of V. The subvarieties of V form a lattice which we denote by ∧(V). In this, the meet A I\ B of two subvarieties A, B is their intersection, and the join A ∨ B is the equational closure of their union, i.e. the smallest subvariety of V that contains A∪ B. A celebrated theorem of B. Jönsson [15] states that if Vis a variety every algebra of which has a distributive congruence lattice then ∧ (V) is distributive. Applying this to the variety O of Ockham algebras, we thus have that ∧(O) is distributive.
Fixed points
Authors: Blyth T S , Varlet J C 
Published: November 2023

Abstract
In an Ockham algebra (L;f) the notion of a fixed point f was introduced in Chapter 2 as an element a ∈L such that f(a) = a. Dually, we say that an element x of an Ockham space (X;g) is a fixed point of g if g(x) = x. We shall denote by Fix L [resp. Fix X] the subset of L [resp. X] formed by the fixed points f [resp. g].
Fixed point separating congruences
Authors: Blyth T S , Varlet J C 
Published: November 2023

Abstract
If (L;f} is an Ockham algebra and x,y are distinct elements of L then we shall say that a congruence , ϑ on L separates x and y if (x, y) ∉ , ϑ. By a fixed point separating congrnence on L we shall mean a congruence that separates every pair of fixed points of L. We shall denote by : ℱ (L) the set of fixed point separating congruences on L. We let Fix L = { αi ; i∈I} be the set of fixed points of (L;/), and we shall assume throughout this chapter that I Fix LI ≥ 2. All of the results that follow appear in [56].
The dual space of a finite simple Ockham algebra
Authors: Blyth T S , Varlet J C 
Published: November 2023

Abstract
We recall that an n-crown (with n; ≥2) is an ordered set C with 2n elements x 1, ... , x2n whose only comparabilities are
An n-crown C is connected, has length 1, |Max 𝒞|𝒞; = |Min 𝒞|= n, every minimal element is covered by two maximal elements, and every maximal element covers two minimal elements; so all vertices of 𝒞 have degree 2. There have been some attempts to generalise this notion. We mention two of these. In [93], W. T. Trotter, Jr. defines a crown Snk as follows : for n ≥ 3 and k ≥ :0, Snk is an ordered set of length 1 with n +; k minimal elements a1, ... , an+k and n + k maximal elements b1, ... , bn+k each a;I being incomparable with bi, ... , bi;+k and being covered by the remaining n - l maximal elements. Here, of course, the subscripts have to be interpreted cyclically. For example, the graph of S42 is as follows :
Relative Ockham algebras
Authors: Blyth T S , Varlet J C 
Published: November 2023

Abstract
In Chapter 1 we gave an affirmative answer to the question of whether every bounded distributive lattice L can be made into an Ockham algebra (L; ∼). If the subvariety V of O to which (L; ∼) has to belong is prescribed, then the answer is far from being affirmative, even when L is finite. For example, as we observed in [41], the 5-element distributive lattice with Hasse diagram [ufig] cannot be made into an M1-algebra since otherwise we would have [ueq] whence either ∼a= l or ∼b = l, so that either ∼2a = 0 or ∼2b = 0 from which it follows by axiom (1) that either a = 0 or b = 0, a contradiction.
Double MS-algebras
Authors: Blyth T S , Varlet J C 
Published: November 2023

Abstract
The notion of a double Stone algebra is well known. This is an algebra (L; ∨ ∧ *,+0,1)of type (2, 2, 1, 1, 0, 0) such that both (L; *) and (L0P; +) are Stone algebras with the unary operations a ⟼a*and a ⟼a+ linked by the properties [ueq] Our objective now is to consider the following natural generalisation.
Subdirectly irreducible double MS-algebras
Authors: Blyth T S , Varlet J C 
Published: November 2023

Abstract
In order to determine the subdirectly irreducible double MS-algebras we can extend the discussion given in Chapter 4 for MS-algebras. Corresponding to the notion of a g-subset in the dual space (X;g) of an MS-algebra (L; 0), we define a {g, h}-subset in the dual space (X; g, h) of a double MS-algebra (L; 0, +) to be a subset of X that is both a g-subset and an h-subset. Such a subset, for example, is gw{x} ∪ hw{ x}. Working with this we see that, corresponding to Corollary 1 of Theorem 4.6, a finite double MS-algebra (L; 0, +) is subdirectly irreducible if and only if there exists x ∈ X such that X = gw{x} ∪ hw{x}.
Singles and Doubles
Authors: Blyth T S , Varlet J C 
Published: November 2023

Abstract
In Chapter 5 we showed that every variety of MS-algebras is characterised by adjoining to the basic axioms of MS at most three from a list of ten identities. If a double MS-algebra (L;0, +) is such that (L;0) satisfies some of these identities then it is natural to ask when (L0P;+) satisfies the same identities. More particularly, if (L;0, +} ∈ DMS and V(L;0) =R, what are the possible subvarieties V(L0P; +)?
A history of the hmneobox
Authors: Walter J. Gehring 
Published: November 2023

Abstract
Almost ten years have passed since the discovery of the homeobox and it seems appropriate to tell the “homeo box story”, how it happened and what advances were made in this field over the past decade. Of course, such accounts are quite subjective and the same events are seen differently by different observers. The discovery of the homeobox was only possible in the congenial atmosphere of a laboratory in which a group of creative and hardworking young scientists made a concerted effort to elucidate the mechanisms of development.
Leader peptidase
Authors: Dalbey R E 
Published: November 2023

Abstract
A temperature-sensitive amber mutation in the leader peptidase gene was isolated after localized mutagenesis. Strain IT41 bearing this mutation accumulates precursor proteins rapidly after a temperature shift to 42°C. Another chromosomal mutation has been constructed in strain H560/pRD9, in which the normal constitutive promoter of the leader peptidase gene is replaced with the inducible arabinose promoter2 Four hours after transfer of this strain to arabinose-free media, precursor proteins begin to accumulate. Protease-mapping and osmotic shock experiments indicated that the precursor to the maltose binding protein is translocated across the plasma membrane and is anchored to the outer surface of the inner membrane. The physiological role of leader peptidase is to release exported proteins from the outer surface of the inner membrane so they can move into the periplasm or to the outer membrane.
KAR2
Authors: Rose M , Vogel J P 
Published: November 2023

Abstract
kar2-1 and all other temperature sensitive (ts·) alleles of KAR2 exhibit defects in nuclear fusion5·8. The ts· mutants can be placed into two classes based on their viability and effects on secretion at the restrictive temperature. Class I alleles (e.g. kar2-159) block translocation of secretory proteins into the lumen of the ER and exhibit a corresponding rapid loss in cell viability at the restrictive temperature. Class II alleles (e.g. kar2-1) do not block secretion but instead result in a variety of post-translocational defects. In contrast to the class I mutants, class II mutants remain viable at the restrictive temperature. Surprisingly, the class II mutant phenotypes are most consistent with a defect in secretory protein processing in the Golgi.
FKB2
Authors: Sykes K 
Published: November 2023

Abstract
The nucleotide sequence of FKB2, isolated from the yeast Saccharomyces cerevisiae, predicts a protein of 135 amino acids, including an N-terminal hydrophobic region that may constitute a 16 (or 17) residue signal sequence12 The mature yeast Fkb2 protein and human FKBP-13 proteins share 55% amino acid sequence identity, and the yeast Fkb2 protein is 52% identical with the yeast cytosolic Fkb1 protein.
SPC18
Authors: Shelness G 
Published: November 2023

Abstract
The nucleotide sequence of SPC 18 cDNA2 (GenBank accession number J05466) encodes a 179 amino acid polypeptide with a calculated molecular mass of 20,626 Da. SPC 18 and SPC 21 (seep. 90) are products of separate genes, yet their amino acid sequences are strikingly similar. In a 176 amino acid region of overlap between the two proteins, no insertions or deletions are present and identity exists at 143 or 81% of amino acid positions. The most dramatic primary structure differences between the two proteins exist at the amino terminus where the SPC 21 primary translation product possesses 11 additional amino acids not present in SPC 18, and in an internal region of the protein where 4 acidic residues in SPC 21 appear as neutral or basic amino acids in SPC 18 (Asp117 to Gin105, Asp120 to His108, Glu131 to Ala119, and Glu140 to Gln128).
α-Glucosidase II
Authors: Trimble R , Morcmcn, K , Herscovics A 
Published: November 2023

Abstract
a-Glucosidase II from rat1 and calf2 liver microsomes and from yeast3 was initially shown to catalyze the specific removal of both glucose residues from Glc2Man9GlcNAc2 Removal of the innermost glucose residue is much slower than that of the terminal glucose. The mannose residues on the upper a-1,6-mannosyl branch of the oligosaccharide are required for enzyme activity3.4. The enzyme readily cleaves aryl a-glucosides and is strongly inhibited by dNJ, N-Me-dNJ, castanospermine, and related compounds5·7 Inhibition by these agents of further processing of oligosaccharides to complex structures is incomplete, in part owing to the ability of some cells to transfer non-glucosylated oligosaccharides to protein8, and in part owing to the action of an endo-a-mannosidase9 (see entry p. 190).
Ca2+ -dependent a-1,2-mannosidase
Authors: Trimble R , Herscovics K Moremen,and A 
Published: November 2023

Abstract
A calcium-activated a-1,2-mannosidase was first partially purified from rabbit liver microsomes and shown to require nonionic detergent or specific phospholipids for activity12. The enzyme removes a-1,2-linked mannose residues from glycoprotein and oligosaccharide substrates. It does not act on aryl a-mannoside, and is inhibited by 1- deoxymannojirimycin (dMNJ) but not by swainsonine3 The purified enzyme is a glycoprotein that migrates on SDS-PAGE as a 52 kDa species. Antibodies have not yet been prepared for immunolocalization studies.
SEC20
Authors: Pelham H 
Published: November 2023

Abstract
Three temperature-sensitive, conditionally-lethal mutant alleles of 5EC20 have been identified. The best characterized of these is sec20-1, which was isolated using a density enrichment screen. At the non-permissive temperature (37°C), this mutant shows a block in secretion at the ER to Golgi step with accumulation of ER and 50nm vesicles2.
SEC7
Authors: Franzusoff A 
Published: November 2023

Abstract
Temperature-sensitive, conditionally lethal sec7 mutants were isolated by a density enrichment protocoI5 Two alle-les, secl-1 and secl-4, appear to exert different effects in disrupting vesicular traffic in the yeast secretory pathway2·6. The accumulation of heterogeneous populations of glycoprotein intermediates in the pathway was observed, ranging from ER to late Golgi forms of the secreted proteins invertase and o:-factor2·. The transport of both soluble and membrane-bound vacuolar enzymes is also disrupted in sec7 yeast at the non-permissive temperature2· s-10_ Multiple species of glycoprotein intermediates were identified (i.e. “leaky” phenotype) even after shifting the cells to 38°C for longer periods before initiating pulse-chase experiments.
KEX2
Authors: Fuller B 
Published: November 2023

Abstract
The DNA sequence of the KEX2 gene (GenBank accession # M24201} predicts an 814 residue polypeptide (90.1 kDa) (see Figure 1) that contains an N-terminal signal peptide and a single transmembrane spanning domain near the Cterminus1A,17. Like subtilisin, the predicted Kex2 polypeptide has the structure of a pre-pro-protein, with a pro-segment of about 90 residues preceding the region of homology to mature subtilisin.
STE13
Authors: Flanagan C A , Thorner J 
Published: November 2023

Abstract
The first allele isolated, ste13-1, was an a-specific sterile mutation that displayed temperature-sensitive mating5 MATa ste13-1 cells were found to secrete, even at 30°C, primarily pro-a-factor containing the -X-Ala- repeats of the spacer sequence2 This aberrant form of secreted pheromone (“a-factor*”) was not biologically active on normal MATa cells, but could be detected using MATa sst2 mutants, which are hypersensitive to pheromone.
DSS4
Authors: Roberts D , Novick P 
Published: November 2023

Abstract
dss4-1 suppresses the growth defect, the block in invertase secretion, and the accumulation of 100 nm secretory vesicles seen in sec4-8 cells at the restrictive temperature1. Suppression is seen at 35°C, but not at 37°C whether dss4-1 is present in single copy or overexpressed. dss4-1 can not suppress a deletion of SEC4 and can not suppress the growth defect of ypt1-1 (seep. 121). dss4-1 has no effect on wild-type SEC4 cells.
A. Protein Translocation And Maturation In The Yeast Er
Authors: Rothblatt J 
Published: November 2023

Abstract
Genetic selections for 5accharomyces cerevisiae mutants exhibiting temperature-sensitive conditional defects in the targeting and translocation of secretory and membrane proteins1 have proved a powerful technique for identifying yeast proteins involved in these processes. in vitro studies of protein import into yeast microsomes initially provided few clues as to the identity of key components. However, such studies did reveal that protein translocation in yeast, by contrast to the situation in mammalian cells, could occur by both co-translational and post-translational mechanisms.
GP-2
Authors: Rindler M J 
Published: November 2023

Abstract
Sequence analysis of a cDNA encoding rat pancreatic GP-2 revealed a protein of 530 amino acids with a predicted 24 residue N-terminal signal sequence and eight potential Nglycosylation sites. The sequence of the canine form is essentially similar. A stretch of 21 hydrophobic amino acids at the (-terminus contains a consensus sequence for attachment of a GPI anchor. The protein is remarkably cysteine-rich, with 28 cysteines present in the mature protein. (GenBank accession nos. M58716, X53935, M37032).