scholarly journals The sublattice of an orthogonal pair in a modular lattice

1979 ◽  
Vol 4 ◽  
Author(s):  
Herbert Gross ◽  
Paul Hafner
Keyword(s):  
Modular Lattice ◽  
Orthogonal Pair

Application of Truncated Multipolar Expansion Pair Functions in Atomic Structure Calculations. II. Irreducible Tensor Operator Form of the Strongly Orthogonal Pair Functions. Reduction of Orthogonality Constraints

1971 ◽  
Vol 49 (1) ◽  
pp. 118-132 ◽  
Author(s):  
K. Jankowski
Keyword(s):  
Closed Shell ◽  
Tensor Operator ◽  
Irreducible Tensor ◽  
Method Of Calculation ◽  
Irreducible Tensor Operator ◽  
Orthogonality Constraints ◽  
Operator Form ◽  
Orthogonal Pair ◽  
Multipolar Expansion ◽  
Pair Function

The truncated multipolar expansion pair functions (TMEPF) defined recently by Jankowski have been used to formulate an approach which takes into account correlation effects within a pair of electrons in the presence of an N electron sea in a closed shell configuration. An irreducible tensor operator form of the strongly orthogonal pair function components has been derived. The analysis of the expressions obtained leads to a systematic reduction of the orthogonality constraints to be imposed on this class of trial functions. The results of this analysis for several types of pair functions have been given. Finally, the method of calculation of matrix elements between orthogonally projected pair function components in terms of radial integrals is presented.

scholarly journals A note on distributive sublattices of a modular lattice

1969 ◽  
Vol 65 (2) ◽  
pp. 219-222 ◽  
Author(s):  
Raymond Balbes
Keyword(s):  
Modular Lattice

scholarly journals A Semimodular Imbedding of Lattices

1960 ◽  
Vol 12 ◽  
pp. 582-591 ◽  
Author(s):  
D. T. Finkbeiner
Keyword(s):  
Modular Lattice ◽  
Dimensional Lattice ◽  
General Lattice ◽  
Basic Properties ◽  
Arithmetic Properties ◽  
Finite Dimensional ◽  
Unpublished Work ◽  
Restricted Type ◽  
Point Lattice

The study of structural or arithmetic properties of a general lattice often can be facilitated by imbedding as a sublattice of a lattice of a more restricted type whose properties are known. However, if is too restricted, a general imbedding is impossible; for example, cannot be modular because , as a sublattice of , would then have to be modular. One of the best results of this nature has been given by Dilworth in an unpublished work in which he shows that any finite dimensional lattice is isomorphic to a sublattice of a semi-modular point lattice (1, pp. 105 and 110). In the present paper Dilworth's imbedding process is modified to obtain a sharper result: Any finite dimensional lattice is isometrically isomorphic to a sublattice of a semi-modular lattice which has the same number of points as and which preserves basic properties of the join-irreducible arithmetic of .

scholarly journals Site-Specific Incorporation of Unnatural Amino Acids into Escherichia coli Recombinant Protein: Methodology Development and Recent Achievement

Biomolecules ◽  
2019 ◽  
Vol 9 (7) ◽  
pp. 255 ◽  
Author(s):  
Sviatlana Smolskaya ◽  
Yaroslav Andreev
Keyword(s):  
Escherichia Coli ◽  
Amino Acids ◽  
Unnatural Amino Acids ◽  
Trna Synthetase ◽  
Nonsense Suppression ◽  
Expression Vectors ◽  
Site Specific ◽  
Suppressor Trna ◽  
E Coli ◽  
Orthogonal Pair

More than two decades ago a general method to genetically encode noncanonical or unnatural amino acids (NAAs) with diverse physical, chemical, or biological properties in bacteria, yeast, animals and mammalian cells was developed. More than 200 NAAs have been incorporated into recombinant proteins by means of non-endogenous aminoacyl-tRNA synthetase (aa-RS)/tRNA pair, an orthogonal pair, that directs site-specific incorporation of NAA encoded by a unique codon. The most established method to genetically encode NAAs in Escherichia coli is based on the usage of the desired mutant of Methanocaldococcus janaschii tyrosyl-tRNA synthetase (MjTyrRS) and cognate suppressor tRNA. The amber codon, the least-used stop codon in E. coli, assigns NAA. Until very recently the genetic code expansion technology suffered from a low yield of targeted proteins due to both incompatibilities of orthogonal pair with host cell translational machinery and the competition of suppressor tRNA with release factor (RF) for binding to nonsense codons. Here we describe the latest progress made to enhance nonsense suppression in E. coli with the emphasis on the improved expression vectors encoding for an orthogonal aa-RA/tRNA pair, enhancement of aa-RS and suppressor tRNA efficiency, the evolution of orthogonal EF-Tu and attempts to reduce the effect of RF1.

scholarly journals Dissecting the Contribution of Release Factor Interactions to Amber Stop Codon Reassignment Efficiencies of the Methanocaldococcus jannaschii Orthogonal Pair

Genes ◽  
2018 ◽  
Vol 9 (11) ◽  
pp. 546 ◽  
Author(s):  
David Schwark ◽  
Margaret Schmitt ◽  
John Fisk
Keyword(s):  
Stop Codon ◽  
Release Factor ◽  
Codon Reassignment ◽  
Methanocaldococcus Jannaschii ◽  
E Coli ◽  
Amber Stop Codon ◽  
Orthogonal Pair ◽  
Amber Codon ◽  
Quantitative Contribution ◽  
Stop Codon Reassignment

Non-canonical amino acids (ncAAs) are finding increasing use in basic biochemical studies and biomedical applications. The efficiency of ncAA incorporation is highly variable, as a result of competing system composition and codon context effects. The relative quantitative contribution of the multiple factors affecting incorporation efficiency are largely unknown. This manuscript describes the use of green fluorescent protein (GFP) reporters to quantify the efficiency of amber codon reassignment using the Methanocaldococcus jannaschii orthogonal pair system, commonly employed for ncAA incorporation, and quantify the contribution of release factor 1 (RF1) to the overall efficiency of amino acid incorporation. The efficiencies of amber codon reassignments were quantified at eight positions in GFP and evaluated in multiple combinations. The quantitative contribution of RF1 competition to reassignment efficiency was evaluated through comparisons of amber codon suppression efficiencies in normal and genomically recoded Escherichia coli strains. Measured amber stop codon reassignment efficiencies for eight single stop codon GFP variants ranged from 51 to 117% in E. coli DH10B and 76 to 104% in the RF1 deleted E. coli C321.ΔA.exp. Evaluation of efficiency changes in specific sequence contexts in the presence and absence of RF1 suggested that RF1 specifically interacts with +4 Cs and that the RF1 interactions contributed approximately half of the observed sequence context-dependent variation in measured reassignment efficiency. Evaluation of multisite suppression efficiencies suggests that increasing demand for translation system components limits multisite incorporation in cells with competing RF1.

scholarly journals 2- and 3-Modular lattice wiretap codes in small dimensions

2015 ◽  
Vol 26 (6) ◽  
pp. 571-590 ◽  
Author(s):  
Fuchun Lin ◽  
Frédérique Oggier ◽  
Patrick Solé
Keyword(s):  
Modular Lattice ◽  
Wiretap Codes

scholarly journals CRITICAL POINTS OF PAIRS OF VARIETIES OF ALGEBRAS

2009 ◽  
Vol 19 (01) ◽  
pp. 1-40 ◽  
Author(s):  
PIERRE GILLIBERT
Keyword(s):  
Natural Number ◽  
Critical Points ◽  
Modular Lattice ◽  
General Theorem ◽  
Finitely Generated ◽  
Congruence Distributive

For a class [Formula: see text] of algebras, denote by Conc[Formula: see text] the class of all (∨, 0)-semilattices isomorphic to the semilattice ConcA of all compact congruences of A, for some A in [Formula: see text]. For classes [Formula: see text] and [Formula: see text] of algebras, we denote by [Formula: see text] the smallest cardinality of a (∨, 0)-semilattices in Conc[Formula: see text] which is not in Conc[Formula: see text] if it exists, ∞ otherwise. We prove a general theorem, with categorical flavor, that implies that for all finitely generated congruence-distributive varieties [Formula: see text] and [Formula: see text], [Formula: see text] is either finite, or ℵn for some natural number n, or ∞. We also find two finitely generated modular lattice varieties [Formula: see text] and [Formula: see text] such that [Formula: see text], thus answering a question by J. Tůma and F. Wehrung.

SU-FF-J-49: Dose Comparsion of MVCB and Orthogonal Pair Portal Images

2006 ◽  
Vol 33 (6Part5) ◽  
pp. 2031-2031
Author(s):  
L Peng ◽  
C Yang ◽  
P Tsai ◽  
Y Chen ◽  
S Sim ◽  
...  
Keyword(s):  
Orthogonal Pair ◽  
Portal Images
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