In this article, we consider the Einstein-scalar field Lichnerowicz equation
-
Δ
u
+
h
u
=
B
u
p
-
1
+
A
u
-
p
-
1
on any connected finite graph
G
=
(
V
,
E
)
, where
A
,
B
,
h
are given functions ...on
V
with
A
≥
0
,
A
≢
0
on
V
, and
p
>
2
is a constant. By using the classical variational method, topological degree theory and heat-flow method, we provide a systematical study on this equation by providing the existence results for each case: positive, negative and null Yamabe-scalar field conformal invariant, namely
h
>
0
,
h
<
0
and
h
=
0
respectively.
Full text
Available for:
EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Abstract
Shaft alignment plays an important role in the installation of ship propulsion shafting, ensuring the safety and reliability of ship propulsion shafting. The article takes the shaft system ...of a 3000m ro-ro ship as an example to simplify the model. Use the workbench platform to perform linear alignment, reasonable alignment and bearing displacement optimization on the shaft system. The results are anastomosis with the results of the traditional three-bending moment algorithm. The optimized displacement result of the bearing can be used as a reference data for shafting installation, which has great practical value.
In this paper, we study the robustness property of policy optimization (particularly Gauss–Newton gradient descent algorithm which is equivalent to the policy iteration in reinforcement learning) ...subject to noise at each iteration. By invoking the concept of input-to-state stability and utilizing Lyapunov’s direct method, it is shown that, if the noise is sufficiently small, the policy iteration algorithm converges to a small neighborhood of the optimal solution even in the presence of noise at each iteration. Explicit expressions of the upperbound on the noise and the size of the neighborhood to which the policies ultimately converge are provided. Based on Willems’ fundamental lemma, a learning-based policy iteration algorithm is proposed. The persistent excitation condition can be readily guaranteed by checking the rank of the Hankel matrix related to an exploration signal. The robustness of the learning-based policy iteration to measurement noise and unknown system disturbances is theoretically demonstrated by the input-to-state stability of the policy iteration. Several numerical simulations are conducted to demonstrate the efficacy of the proposed method.
Full text
Available for:
EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Due to their large strain capability, dielectric elastomers are promising materials for application as transducers in cameras, robots, valves, pumps, energy harvesters, and so on. The dielectric ...elastomer transducers are based on the deformation of a soft polymer membrane contracting in thickness and expanding in area, induced by the application of a voltage across the two compliant electrodes coated on both sides of the membrane. This paper focuses on the static large deformation analysis of a dielectric elastomer membrane--spring system. The system is constructed from attaching a disk in the middle of a circular dielectric membrane and then connecting the disk with a spring. This configuration can be potentially used as a key part in valves. The basic governing equations describing the large out-of-plane deformations are formulated, and the obtained equations are solved numerically. The relations related to the displacement of the disk, the spring force, the applied voltage, and the parameters of spring including stiffness and initial length are illustrated. The results show that the anticipated displacement of the disk can be controlled by adjusting either or both of the parameters of the spring and the applied voltage. In addition, the parameters of the spring, that is, the stiffness and the initial length, play an important role in the performance of the membrane--spring system.
Abstract
Background
Dominance and other non-additive genetic effects arise from the interaction between alleles, and historically these phenomena play a major role in quantitative genetics. However, ...most genome-wide association studies (GWAS) assume alleles act additively.
Results
We systematically investigate both dominance—here representing any non-additive within-locus interaction—and additivity across 574 physiological and gene expression traits in three mammalian stocks: F2 intercross pigs, rat heterogeneous stock, and mice heterogeneous stock. Dominance accounts for about one quarter of heritable variance across all physiological traits in all species. Hematological and immunological traits exhibit the highest dominance variance, possibly reflecting balancing selection in response to pathogens. Although most quantitative trait loci (QTLs) are detectable as additive QTLs, we identify 154, 64, and 62 novel dominance QTLs in pigs, rats, and mice respectively that are undetectable as additive QTLs. Similarly, even though most cis-acting expression QTLs are additive, gene expression exhibits a large fraction of dominance variance, and trans-acting eQTLs are enriched for dominance. Genes causal for dominance physiological QTLs are less likely to be physically linked to their QTLs but instead act via trans-acting dominance eQTLs. In addition, thousands of eQTLs are associated with alternatively spliced isoforms with complex additive and dominant architectures in heterogeneous stock rats, suggesting a possible mechanism for dominance.
Conclusions
Although heritability is predominantly additive, many mammalian genetic effects are dominant and likely arise through distinct mechanisms. It is therefore advantageous to consider both additive and dominance effects in GWAS to improve power and uncover causality.
The superposition formulas of multi-solutions to the (3+1)-dimensional generalized shallow water wave-like Equation (GSWWLE) are proposed. There are arbitrary test functions in the superposition ...formulas of the mixed solutions and the interaction solutions, and we generalized to the sum of any N terms. By freely selecting the test functions and the positive integer N, we have obtained abundant solutions for the GSWWLE. First, we introduced new mixed solutions between two arbitrary functions and the multi-kink solitons, and the abundant mixed solutions were obtained through symbolic computation. Next, we constructed the multi-localized wave solutions which are the superposition of N-even power functions. Finally, the novel interaction solutions between the multi-localized wave solutions and the multi-arbitrary function solutions for the GSWWLE were obtained. The evolution behaviors of the obtained solutions are shown through 3D, contour and density plots. The received results have immensely enriched the exact solutions of the GSWWLE in the available literature.
Thousands of QTLs for meat quality traits have been identified by linkage mapping studies, but most of them lack precise position or replication between populations, which hinder their application in ...pig breeding programs. To localize QTLs for meat quality traits to precise genomic regions, we performed a genome-wide association (GWA) study using the Illumina PorcineSNP60K Beadchip in two swine populations: 434 Sutai pigs and 933 F2 pigs from a White Duroc×Erhualian intercross. Meat quality traits, including pH, color, drip loss, moisture content, protein content and intramuscular fat content (IMF), marbling and firmness scores in the M. longissimus (LM) and M. semimembranosus (SM) muscles, were recorded on the two populations. In total, 127 chromosome-wide significant SNPs for these traits were identified. Among them, 11 SNPs reached genome-wise significance level, including 1 on SSC3 for pH, 1 on SSC3 and 3 on SSC15 for drip loss, 3 (unmapped) for color a*, and 2 for IMF each on SSC9 and SSCX. Except for 11 unmapped SNPs, 116 significant SNPs fell into 28 genomic regions of approximately 10 Mb or less. Most of these regions corresponded to previously reported QTL regions and spanned smaller intervals than before. The loci on SSC3 and SSC7 appeared to have pleiotropic effects on several related traits. Besides them, a few QTL signals were replicated between the two populations. Further, we identified thirteen new candidate genes for IMF, marbling and firmness, on the basis of their positions, functional annotations and reported expression patterns. The findings will contribute to further identification of the causal mutation underlying these QTLs and future marker-assisted selection in pigs.
Full text
Available for:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
In this letter, the problem of moving a gantry crane with a flexible cable and a sway range constraint to the desired position is solved. The dynamic model of the flexible gantry crane system is ...built based on the absolute nodal coordinate formulation (ANCF), which is useful for analyzing flexible bodies. A novel controller is proposed to control the gantry crane to the desired position and guarantee the sway range constraint. Moreover, with the help of an eye-in-hand camera, an adaptive law is developed to detect the position of the object with respect to the base frame. The convergence of the cable's position to the desired position, the satisfaction of the sway range constraint, and the convergence of the estimated object's position to the real value are rigorously verified based on the Lyapunov theory. Simulation demonstrates the effectiveness of the proposed controller.
A novel transverse flux linear synchronous motor (TFLSM) realizes the integrated functions of propulsion, levitation, and guidance for maglev trains. An efficient and reliable electromagnetic force ...calculation method is required at the initial stage of TFLSM topology design to assess the conformability to the intended application requirements. The research dimension of the proposed motor needs to be extended from the one-dimensional (1-D) space to the three-dimensional (3-D) space. With respect to constructing the mapping relationship between electromagnetic parameters and dimensional structures, the 3-D magnetic circuit method is deservedly convenient. A dynamic magnetic circuit grid model considering the actual operating conditions of the maglev motor is proposed in this article. First, the basic configuration and operation principle of the TFLSM are described. Second, a 3-D magnetic circuit model is established to analyze and calculate the electromagnetic force characteristics of TFLSM. The 3-D forces of TFLSM under different specification parameters are analyzed. Third, finite element analysis and prototype TFLSM experiments are carried out to validate the correctness of the theoretical analysis.
PDF
