Alternative Rings Research Articles

Thermal Formation of Metathesis-Active Tungsten Alkylidene Complexes from Cyclohexene.

A 7-tungstabicyclo[4.3.0]nonane complex forms slowly upon addition of cyclohexene to the ethylene complex, W(NAr)(OSiPh3)2(C2H4), at 22 °C. A single-crystal X-ray study showed its structure to be closest to a square pyramid (τ = 0.23). At 22 °C, loss of cyclohexene or ring contraction of the 7-tungstabicyclo[4.3.0]nonane complex is slow. Above ∼80 °C, cyclohexene is ejected to give W(NAr)(OSiPh3)2(C2H4), but a sufficient amount of 7-tungstabicyclo[4.3.0]nonane complex remains in the presence of cyclohexene and the ring contracts to yield methylenecyclohexane and a methylidene complex or ethylene and a cyclohexylidene complex. Other complexes that have been observed include an 8-tungstabicyclo[4.3.0]nonane complex formed from 1,7-octadiene, a 7-tungstabicyclo[4.2.0]octane complex (formed from a methylidene complex and cyclohexene), and a methylenecyclohexane complex. 13C-Labeling studies show that the exo-methylene group in methylenecyclohexane and the α positions in the 8-tungstabicyclo[4.3.0]nonane come from ethylene. An alternative ring contraction of a tungstacyclopentane made from two molecules of cyclohexene cannot be excluded when concentrations of ethylene are low. A cyclohexylidene complex could also form from two cyclohexenes via a newly proposed "alkyl/allyl" mechanism. The results reported here are the first experimental confirmations that a tungstacyclopentane can ring-contract thermally at a substituted WCα position to form a tungstacyclobutane and therefore metathesis-active alkylidenes.

Results on Commutativity for Alternative Rings With 2, 3-Torsion Free.

ABSTRACT In this article, we establish and proof some theorem on commutativity of alternative ring with 2, 3 –torsion free satisfy the following properties (Identities): (P1) [x2y2+y2x2,x]=0 (p2) [x(xy)2+(xy)2x,x]=0 (p3) [x(x2y2),x]=0 (p4) [x(xy),x]=0 for every x,y in R. Keywords: .

Commuting maps and identities with inverses on alternative division rings

Let D be an alternative division ring with characteristic different from two. The purpose of this paper is to characterize additive mappings f,g:D→D satisfying certain identities studied by Vukman, Brešar, and Catalano previously on an associative division ring. We also present some new identities concerning Lie and Jordan products, and provide a complete description of commuting maps on octonion algebras.

Comparison of Pericardial and Prosthetic Rings for Mitral Repair: Are Pericardial Rings Durable in the Mid- to Long-Term Follow Up?

While prosthetic rings are commonly used for mitral valve repairs, autologous pericardium is an alternative ring material that can be used in these procedures. In this report, we aim to present a comparison of two types of rings used for mitral repair. Between January 2005 and January 2009, 107 patients who underwent mitral valve repair surgery were analyzed. Patients were divided into two groups, according to the type of ring that was used for mitral annular stabilization. Glutaraldehyde-treated pericardial rings were used for 31 patients (group 1), whereas prosthetic rings were used for 76 patients (group 2). Survival, freedom from reoperation, recurrent mitral regurgitation, and the effects of rheumatic mitral disease on these parameters were evaluated and compared for both groups. Follow-up time for our cohort was 4.24±0.4 years. There were four and seven late mortalities in groups 1 and 2, respectively, and five reoperations in each group. There was no significant difference between the groups, in terms of survival, freedom from reoperation, and recurrent mitral regurgitation (log-rank analyses for both groups were P = 0.777, P = 0.346, and P = 0.781, respectively). There was no significant difference in freedom from reoperation and recurrent mitral regurgitation for both groups, in terms of underlying rheumatic valvular disease and other types of pathology. Pericardial ring annuloplasty shows to be a considerable alternative technique for mitral valve repair procedures in the mid- to long-term follow up. Rheumatic mitral valves had poor outcomes, when compared with other types of structural valvular pathologies in cases where pericardial rings were used in the repair procedure.

Alternative ring flange models for buckling verification of tubular steel wind turbine towers via advanced numerical analyses and comparison to code provisions

The beneficial effect of ring flanges between adjacent sections of tubular steel wind turbine t6owers to their susceptibility to local shell buckling is investigated by means of linear and nonlinear buckling finite element analyses, using alternative numerical models. Models comprising solid vs shell elements for the tower shell and solid vs shell vs beam elements for the ring flanges are compared, leading to similar results. Thus, computational cost is adopted as the deciding factor towards preferring the simpler and lighter models. Then, the behavior of an approximately 120 m tall wind turbine tower under realistic wind and gravity loads is investigated, focusing on the buckling response of successive configurations of sections of the tower below each flange, in order to assess the buckling potential throughout the tower height and compare to analytical buckling verification procedures proposed in EN1993-1-6. Nonlinear finite element analyses considering geometrical and material nonlinearity and imperfections with the shape of the three primary buckling modes are employed. The imperfection size is determined according to EN1993-1-6 for fabrication quality class A, B or C. Moreover, a parametric investigation of the thicknesses of ring flanges between consecutive tower sections indicates significant margins for thickness reduction in terms of the flanges’ ability to act as stiffeners for preventing local buckling.

Multiplicative Jordan n-higher derivations on alternative rings containing idempotents

Suppose [Formula: see text] is an alternative ring containing a non-trivial idempotent and [Formula: see text] be a mapping from [Formula: see text] into itself. In this paper, we study the Jordan n-higher derivations on alternative rings and prove that under some mild conditions every multiplicative Jordan n-higher derivations on [Formula: see text] is additive. It is to be noted that the similarity to the notions is only in its written form, but not in its theoretical structures, because the Pierce decomposition used in the results for alternative rings is the generalization of the Pierce decomposition for associative rings.

Impact of disturbance signatures on tree-ring width and blue intensity chronology structure and climatic signals in Carpathian Norway spruce

Tree radial growth is influenced by climatic and various non-climatic factors, which can complicate the extraction of climate signals from tree rings. We investigated the influence of disturbance on tree-ring width (RW) and latewood blue intensity (BI) chronologies of Norway spruce from the Carpathian Mountains to explore the extent to which disturbance can affect temperature signals in tree rings. Overall, ∼15000 high-elevation Norway spruce tree cores from 34 sites grouped into four regions (Slovakia, Ukraine, North and South Romania) were analyzed. The curve intervention detection (CID) method was applied to detect and correct identified disturbance trends. RW chronology structural comparisons were performed among disturbance-affected and disturbance-corrected chronologies for various spatial (regional / site) scales and sampling subsets. Structural comparisons were also performed for RW and BI chronologies developed from separate groups of series (i.e., disturbed, and undisturbed) for five sites exhibiting clear disturbance trends. Temperature sensitivity was assessed for all chronology variants of both parameters. We found that disturbance trends only affected RW chronologies at the site/subset scale with relatively small series replication and were not detected at the regional scale. Unlike RW, BI chronologies were generally unaffected by disturbance. BI data also contained much stronger growing season temperature signals, which appeared to be both spatially and temporally more coherent. Whereas highly replicated and spatially extensive datasets can help minimize or eliminate disturbance trends in RW chronologies, this potential influence should be considered when interpreting climatic signals in tree rings and reconstructing historical climate in weakly replicated periods. On the other hand, BI is a promising alternative tree ring parameter with stronger and more stable growing season temperature signals, whose seemingly disturbance-free chronology structure does not appear to suffer from this ecological bias, and therefore represents a more suitable parameter for dendroclimatological research.

A note on radicals of associative rings and alternative rings

A note on radicals of associative rings and alternative rings

Alternative rings whose associators are not zero-divisors

The purpose of this short note is to prove that if R is an alternative ring whose associators are not zero-divisors, then R has no zero-divisors. By a result of Bruck and Kleinfeld, if, in addition, the characteristic of R is not 2, then the central quotient of R is an octonion division algebra over some field.

A short characterization of the octonions

In this article, we prove that if R is a proper alternative ring whose additive group has no 3-torsion and whose non-zero commutators are not zero-divisors, then R has no zero-divisors. It follows from a theorem of Bruck and Kleinfeld that if, in addition, the characteristic of R is not 2, then the central quotient of R is an octonion division algebra over some field. We include other characterizations of octonion division algebras and we also deal with the case where has 3-torsion.

Synthesis of representative critical path circuits considering BEOL variations for deep sub-micron circuits

The proportion of interconnect delay in the critical path on a chip is increasing and becomes over 20% in sub-10nm technologies, which means in order to capture post-Si performance accurately, the representative critical path circuit should reflect not only FEOL (front-end-of-line) but also BEOL (back-end-of-line) variations. Since the number of BEOL metal layers exceeds ten and the layers have variation on resistance and capacitance intermixed with resistance variation on vias between them, a very high dimensional design space exploration is necessary to synthesize a representative critical path circuit which is able to provide an accurate performance prediction. To this end, we propose a BEOL-aware methodology of synthesizing a representative critical path circuit, which is able to incrementally explore, starting from an initial path circuit on the post-Si target circuit, routing patterns (i.e., BEOL reconfiguring) as well as gate resizing on the path circuit. Precisely, our synthesis framework of critical path circuit integrates a set of novel techniques: (1) extracting and classifying BEOL configurations for lightening design space complexity, (2) formulating BEOL random variables for fast and accurate timing analysis, and (3) exploring alternative (ring oscillator) circuit structures for extending the applicability of our work. In summary, our synthesis framework is able to reduce the prediction error by 54% and 19% on average over that using the conventional critical path replica and using the conventional method exploiting gate sizing only, respectively.

Lie maps on alternative rings preserving idempotents

Let $\Re$ and $\Re'$ unital $2$,$3$-torsion free alternative rings and $\varphi: \Re \rightarrow \Re'$ be a surjective Lie multiplicative map that preserves idempotents. Assume that $\Re$ has a nontrivial idempotents. Under certain assumptions on $\Re$, we prove that $\varphi$ is of the form $\psi + \tau$, where $\psi$ is either an isomorphism or the negative of an anti-isomorphism of $\Re$ onto $\Re'$ and $\tau$ is an additive mapping of $\Re$ into the centre of $\Re'$ which maps commutators into zero.

4-Transitivity and Cross-Ratio in Moufang-Klingenberg Planes over Rings of Plural Numbers

In this paper, we carry the obtained results for a certain class of Moufang-Klingenberg planes co-ordinatized by the local alternative ring of dual numbers, over to a class of Moufang-Klingenberg planes coordinatized by the plural algebra of order m which is a local alternative ring. So, we show that its collineation group is transitive on quadrangles and therefore that coordinatization of the planes is independent of the choice of the coordinatization quadrangle. Moreover, by a conjugacy class we discuss the definition of cross-ratio of four distinct points on the projective lines for the planes.

Commuting maps on alternative rings

Suppose $\mathfrak{R}$ is a $2$,$3$-torsion free unital alternative ring having an idempotent element $e_1$ $\left(e_2 = 1-e_1\right)$ which satisfies $x \mathfrak{R} \cdot e_i = \{0\} \rightarrow x = 0$ $\left(i = 1,2\right)$. In this paper, we aim to characterize the commuting maps. Let $\varphi$ be a commuting map of $\mathfrak{R}$ so it is shown that $\varphi(x) = zx + \Xi(x)$ for all $x \in \mathfrak{R}$, where $z \in \mathcal{Z}(\mathfrak{R})$ and $\Xi$ is an additive map from $\mathfrak{R}$ into $\mathcal{Z}(\mathfrak{R})$. As a consequence a characterization of anti-commuting maps is obtained and we provide as an application, a characterization of commuting maps on von Neumann algebras relative alternative $C^{*}$-algebra with no central summands of type $I_1$.

Synthesis, Characterization and Docking Study of Novel Pyrimidine Derivatives as Anticancer Agents

New compounds 5 and 9 using DNA bases e.g. Adenine 1 and Guanine 6 derivatives have been synthesized. The use of simple methods to synthesize compounds 5 and 9 were done using pyrimidine as an alternative DNA base ring. Another design to synthesize new simple pyrimidine rings utilizing thiourea and ethylcyano acetate to afford 6-amino-2-thiouracil was adopted. The reaction of thiouracil 10 with chloro cyano or chloro ester and ketone, resulted in the formation of adduct compounds 18-21, rather than the formation of compound 17. All the synthesized compounds were subjected to docking study, in order to gain insights into their binding modes against cyclin-dependent protein kinase 2 (CDK-2) that is involved heavily in cell cycle regulation and receptor protein B-cell lymphoma 2 (BCL-2) which is involved in cell apoptosis. These targets were selected based on their key roles in cancer progression via the regulation of the cell cycle and DNA replication. Molecular-docking analyses showed that compound 14e was the best docked ligand against both targets, as it displayed the lowest binding energy, critical hydrogen bonds and hydrophobic interactions with the targets.

Variations on a Theme of Glauberman

A new and elementary proof of the Artin–Zorn theorem that finite alternative division rings are fields is given. The characterisation of finite fields of Glauberman and Heimbeck is also extended to a broader class of fields, the two subjects being connected via geometry.

Multiplicative Lie-type derivations on alternative rings

Let be an alternative ring containing a nontrivial idempotent and be a multiplicative Lie-type derivation from into itself. Under certain assumptions on we prove that is almost additive. Let be the -th commutator defined by n indeterminates If is a unital alternative ring with a nontrivial idempotent and is -torsion free, it is shown under certain condition of and that where δ is a derivation and such that for all

A coaxial film capacitor with a novel structure to enhance its flashover performance.

As one of the key components of an electromagnetic pulse simulator, the peaking capacitor is coaxially constructed with a laminate structure utilizing alternative thin metal rings and polymer film dielectrics, which is designed as a part of the antenna. This paper presents a coaxial film capacitor with a novel structure to improve its flashover performance. First, the relationship between the capacitance and the capacitor's structural parameters are deduced, and a theoretical basis of lengthening the polymer film dielectrics to enhance the flashover performance is discussed. Based on the theoretical analysis, two 150 pF, 3-layer coaxial film capacitors with different extended lengths for the polymer film dielectrics (10 and 60 mm) are designed and developed. For the capacitor with a 60 mm extended film dielectric, the polymethylmethacrylate rings are adhered to the thin metal rings to support the polymer film dielectrics using a soft adhesive. Electric field analyses show that a longer extended length could decrease the surface field at the edge of the polymer film dielectric by as much as 93%. Comparative insulation experiments show that the flashover voltage for the improved capacitor is 89.9% higher than the original one. The influence of the capacitor's polymer extensions (including the polymer supporting rings and the film dielectrics) on the radiating field of a cone antenna is analyzed numerically, and the results show that only slight changes are introduced into the radiating field. Finally, a designed 350 pF, 20-layer coaxial film capacitor with lengthened film dielectrics is presented.

Commutative part of skew polynomial ring over split-octonion

Let R be a ring. The set of polynomials R[x: σ] forms a ring with multiplication rule σ(a)x for all a ∈ R where σ is an endomorphism on R. In this paper R is the ring split octonion. Split octonion is an anti-commutative 8-dimensional alternative ring. In this paper, the commutative part of that ring over spilt octonion ring is determined.

Lie maps on alternative rings

Let $${\mathfrak {R}}\, $$ be an alternative ring containing a nontrivial idempotent and $${\mathfrak {R}}\, '$$ be another alternative ring. Suppose that a bijective mapping $$\varphi : {\mathfrak {R}}\, \rightarrow {\mathfrak {R}}\, '$$ is a Lie multiplicative mapping and $${\mathfrak {D}}\, $$ is a Lie triple derivable multiplicative mapping from $${\mathfrak {R}}\, $$ into $${\mathfrak {R}}\, $$. Under a mild condition on $${\mathfrak {R}}\, $$, we prove that $$\varphi $$ and $${\mathfrak {D}}\, $$ are almost additive, that is, $$\varphi (a + b) - \varphi (a) - \varphi (b) \in \mathcal {Z}({\mathfrak {R}}\, ')$$ and $${\mathfrak {D}}\, (a+b) - {\mathfrak {D}}\, (a) - {\mathfrak {D}}\, (b) \in \mathcal {Z}({\mathfrak {R}}\, )$$ for all $$a,b \in {\mathfrak {R}}\, $$, where $$\mathcal {Z}({\mathfrak {R}}\, ')$$ is the commutative centre of $${\mathfrak {R}}\, '$$ and $$\mathcal {Z}({\mathfrak {R}}\, )$$ is the commutative centre of $${\mathfrak {R}}\, $$. As applications, we show that every Lie multiplicative bijective mapping and Lie triple derivable multiplicative mapping on prime alternative rings are almost additive.