Representations of hom-Lie algebras

In this paper, we study representations of hom-Lie algebras. In particular, the adjoint representation and the trivial representation of hom-Lie algebras are studied in detail. Derivations, deformations, central extensions and derivation extensions of hom-Lie algebras are also studied as an application.Comment: 16 pages, multiplicative and regular hom-Lie algebras are used, Algebra and Representation Theory, 15 (6) (2012), 1081-109

Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras

The purpose of this paper is to investigate ternary multiplications constructed from a binary multiplication, linear twisting maps and a trace function. We provide a construction of ternary Hom-Nambu and Hom-Nambu-Lie algebras starting from a binary multiplication of a Hom-Lie algebra and a trace function satisfying certain compatibility conditions involving twisting maps. We show that mutual position of kernels of twisting maps and the trace play important role in this context, and provide examples of Hom-Nambu-Lie algebras obtained using this construction

Cohomology and Deformations of nn-Lie algebra morphisms

The study of $n$-Lie algebras which are natural generalization of Lie algebras is motivated by Nambu Mechanics and recent developments in String Theory and M-branes. The purpose of this paper is to define cohomology complexes and study deformation theory of $n$-Lie algebra morphisms. We discuss infinitesimal deformations, equivalent deformations and obstructions. Moreover, we provide various examples

Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras

In this paper we construct ternary $q$-Virasoro-Witt algebras which $q$-deform the ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos using $su(1,1)$ enveloping algebra techniques. The ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos depend on a parameter and are not Nambu-Lie algebras for all but finitely many values of this parameter. For the parameter values for which the ternary Virasoro-Witt algebras are Nambu-Lie, the corresponding ternary $q$-Virasoro-Witt algebras constructed in this article are also Hom-Nambu-Lie because they are obtained from the ternary Nambu-Lie algebras using the composition method. For other parameter values this composition method does not yield Hom-Nambu Lie algebra structure for $q$-Virasoro-Witt algebras. We show however, using a different construction, that the ternary Virasoro-Witt algebras of Curtright, Fairlie and Zachos, as well as the general ternary $q$-Virasoro-Witt algebras we construct, carry a structure of ternary Hom-Nambu-Lie algebra for all values of the involved parameters

Postoperative Pain: Factors and Tools to Improve Pain Management in Children

Outpatient surgery has made it increasingly common for parents to manage pain in the home setting. Studies have shown that parents often under treat pain, leaving children vulnerable to the negative side effects of suboptimal pain management. Multiple factors affect pain management like child’s age and developmental stage, language, cultural values like stoicism, parental beliefs about medication, biological differences among groups, etc. Understanding all the factors involved can help healthcare providers and parents better understand pain and contribute to optimal pain management. Multiple tools and technological interventions have been created to help create a better understanding of pain and a holistic approach to care

Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras

We present a procedure to construct (n+1)-Hom-Nambu-Lie algebras from n-Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n+k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions

Study of the nanocrystalline bulk Al alloys synthesized by high energy mechanical milling followed by room temperature high pressing consolidation

AbstractIn the present study high energy mechanical milling followed by high-pressing consolidation has been used to obtain bulk nanocrystalline Al-Fe-Si alloy. Quantitative XRD analysis and scanning electron microscopy were used to characterize the material evolution during thermal treatments in the temperature range 25–500∘C. The cold-worked structure have been synthesized with microstructure showing a mixture of a significant low size of crystallite (70 nm) and a high level of lattice strains (0.85%). Starting from the nanocrystalline specimens, isochronal experiments were carried out to monitor the reserve microstructure and transformations. The high temperature annealing is required for ameliorating the quality of room temperature consolidated materials by removing all porosity and obtaining good interparticle bonding. The thermal conductivity and the thermal diffusivity are investigated with the Photothermal deflection technique. These thermal parameters increase with the annealing temperatures. This behavior is attributed to the increase in the rate of diffusion coefficient of added elements inside the aluminum matrix

Contractions of low-dimensional nilpotent Jordan algebras

In this paper we classify the laws of three-dimensional and four-dimensional nilpotent Jordan algebras over the field of complex numbers. We describe the irreducible components of their algebraic varieties and extend contractions and deformations among them. In particular, we prove that J2 and J3 are irreducible and that J4 is the union of the Zariski closures of two rigid Jordan algebras.Comment: 12 pages, 3 figure

Changing Healthcare Provider and Parent Behaviors in the Pediatric Post‐Anesthesia‐Care‐Unit to Reduce Child Pain: Nurse and Parent Training in Postoperative Stress (NP‐TIPS)

Background Children who undergo surgery experience significant pain in the post anesthesia care unit. Nurse and parent behaviors in the post anesthesia care unit directly impact child postoperative pain. Therefore, we have developed and evaluated (Phase 1) and then tested (Phase 2) the feasibility of a new intervention (Nurse and Parent Training in Postoperative Stress) to alter parent and nurse behaviors in a way consistent with reducing child postoperative pain. Methods In Phase 1, a multidisciplinary team of experts (physicians, nurses, and psychologists) developed an empirically‐based intervention which was then evaluated by experienced nurses (N = 8) and parents (N = 9) during focus groups. After revising the intervention based on focus group feedback, it was tested in Phase 2 using a pre‐post study design. Nurses (N = 23) who worked in the recovery room were recruited to be part of both pre‐ and post‐intervention data collection periods. Parents were recruited to be part of either the pre‐ (N = 52) or post‐intervention (N = 60) data collection periods. Nurses and parent‐child dyads were recorded in the post anesthesia care unit and videos were coded for the desired (i.e., behaviors that may decrease child pain) and non‐desired (i.e., behaviors that may increase child pain) behaviors. Pain data was collected from the children\u27s medical records to assess pain after surgery. The intervention was given to the nurses and parents in the post‐intervention data collection period. Results Nurses significantly increased their rate of desired behaviors by 231% (p = 0.001; Somer\u27s D = 1) and significantly decreased their rate of non‐desired behaviors by 62% (p = 0.004, Somer\u27s D = ‐0.88, 95% CI [‐1.74, ‐0.03]). Parents significantly increased their rate of desired behaviors by 124% (p = 0.033). Moreover, the intervention significantly decreased child pain in the post anesthesia care unit (b = ‐2.19, SE = 0.63, z = ‐3.46, p = .001, 95%CI [‐3.43, ‐0.95]). Conclusions The intervention was effective in changing nurse and parent behaviors as well as child pain after surgery