On the remarkable relations among PDEs integrable by the inverse spectral transform method, by the method of characteristics and by the Hopf-Cole transformation

We establish deep and remarkable connections among partial differential equations (PDEs) integrable by different methods: the inverse spectral transform method, the method of characteristics and the Hopf-Cole transformation. More concretely, 1) we show that the integrability properties (Lax pair, infinitely-many commuting symmetries, large classes of analytic solutions) of (2+1)-dimensional PDEs integrable by the Inverse Scattering Transform method ($S$-integrable) can be generated by the integrability properties of the (1+1)-dimensional matrix B\"urgers hierarchy, integrable by the matrix Hopf-Cole transformation ($C$-integrable). 2) We show that the integrability properties i) of $S$-integrable PDEs in (1+1)-dimensions, ii) of the multidimensional generalizations of the GL(M,\CC) self-dual Yang Mills equations, and iii) of the multidimensional Calogero equations can be generated by the integrability properties of a recently introduced multidimensional matrix equation solvable by the method of characteristics. To establish the above links, we consider a block Frobenius matrix reduction of the relevant matrix fields, leading to integrable chains of matrix equations for the blocks of such a Frobenius matrix, followed by a systematic elimination procedure of some of these blocks. The construction of large classes of solutions of the soliton equations from solutions of the matrix B\"urgers hierarchy turns out to be intimately related to the construction of solutions in Sato theory. 3) We finally show that suitable generalizations of the block Frobenius matrix reduction of the matrix B\"urgers hierarchy generates PDEs exhibiting integrability properties in common with both $S$- and $C$- integrable equations.Comment: 30 page

Wanprestasi Pembayaran Klaim Asuransi Jiwa Akibat Kelalaian Penyerahan Berkas oleh Mitra Penanggung sebagai Kolektor Pengajuan Klaim (Studi Kasus Sertifikat Asuransi Polis Nomor 15.001673)

At this time many banks are incentive to lure consumer credit to consumers. In general, consumer loan interest rate is higher than productive credit, even there is a fixed rate. It seems that the fixed rate makes it easy to organize family finances, paying only monthly installments of the same amount, but if carefully calculated, the interest is much higher. Consumer Loan Protection with Insurance Policy Certificate 15.001673 is a life insurance product that guarantees repayment of the remaining amount of Loans and / or monthly loan installment of the Customer as Participant (Insured) to the Policyholder in case the Participant (the Insured) has a death risk or total temporary disability / Or total permanent disability. Although it is clear about the rights and obligations in the insurance agreement but the reality is very different because it turns out the insurer does not fulfill its obligations in the event of claim submission from the insured. Rejection of insurance claims may be made by the insurer under the pretext of submitting the file beyond the specified time limit. Issues to be studied further is how validation of denial of life insurance claim made by Jasindo in accordance with the insurance policy and existing legislation and whether Partner Error is can be classified as Wanprestasi payment of Insurance Claim for late in submission of policy file No: 15.001673. In conducting research, this research is normative law research that is research having object of study about rule or rule. The objective is to determine the validity of the refusal of insurance claims made by Jasindo in accordance with the existing insurance policies and regulations and to find out the Default Payment of Insurance Claims due to Delayed Submission by Marketing Party as Collector Submission of Claim on Insurance Certificate Number 15.00167

Integrable lattices and their sublattices II. From the B-quadrilateral lattice to the self-adjoint schemes on the triangular and the honeycomb lattices

An integrable self-adjoint 7-point scheme on the triangular lattice and an integrable self-adjoint scheme on the honeycomb lattice are studied using the sublattice approach. The star-triangle relation between these systems is introduced, and the Darboux transformations for both linear problems from the Moutard transformation of the B-(Moutard) quadrilateral lattice are obtained. A geometric interpretation of the Laplace transformations of the self-adjoint 7-point scheme is given and the corresponding novel integrable discrete 3D system is constructed.Comment: 15 pages, 6 figures; references added, some typos correcte

Dressing method based on homogeneous Fredholm equation: quasilinear PDEs in multidimensions

In this paper we develop a dressing method for constructing and solving some classes of matrix quasi-linear Partial Differential Equations (PDEs) in arbitrary dimensions. This method is based on a homogeneous integral equation with a nontrivial kernel, which allows one to reduce the nonlinear PDEs to systems of non-differential (algebraic or transcendental) equations for the unknown fields. In the simplest examples, the above dressing scheme captures matrix equations integrated by the characteristics method and nonlinear PDEs associated with matrix Hopf-Cole transformations.Comment: 31 page

Combination of inverse spectral transform method and method of characteristics: deformed Pohlmeyer equation

We apply a version of the dressing method to a system of four dimensional nonlinear Partial Differential Equations (PDEs), which contains both Pohlmeyer equation (i.e. nonlinear PDE integrable by the Inverse Spectral Transform Method) and nonlinear matrix PDE integrable by the method of characteristics as particular reductions. Some other reductions are suggested.Comment: 12 page

Impact on help-seeking behaviours of a campaign perceived to decrease stigma and increase openness around mental health

Issue Addressed: There is considerable evidence that public stigma around mental illness inhibits help-seeking for mental health problems. Hence there have been many interventions and campaigns designed to reduce stigma around mental illness. However, as far as could be ascertained, none of these stigma reduction interventions has reported any substantial impact of reducing stigma on people\u27s mental health help-seeking behaviours. The aim of this paper is to report on the impact of the Act-Belong-Commit positive mental health promotion Campaign on help-seeking via increasing perceived openness around mental health and reducing perceived stigma around mental illness. Methods: State-wide computer assisted telephone interviews (CATIs) of the general adult population were undertaken in 2018 and 2019 (N = 600 adults per year). The questionnaire included measures of respondents\u27 awareness of the Act-Belong-Commit Campaign, their beliefs about the Campaign\u27s impact on mental illness stigma and openness around mental health issues, and whether they had sought help for or information about a mental health problem as a result of their exposure to the Campaign. Results: Those who believed the Act-Belong-Commit Campaign increased openness around mental health issues were significantly more likely than those not holding this belief to have sought information about mental health and to have sought help for a mental health problem as a result of their exposure to the Campaign. Those who believed the Act-Belong-Commit Campaign decreased stigma around mental illness versus those not holding this belief were significantly more likely to have sought information, and more likely, but not significantly so, to have sought help as a result of their exposure to the Campaign. Overall, the effect was slightly greater for increased openness. Conclusion: As far as we are aware, these are the first reported findings of a positive impact on mental health help-seeking behaviours as a result of a population-wide mental health promotion Campaign being seen to have increased openness around mental health and decreased stigma around mental illness. So What?: These findings suggest that accompanying specific stigma reduction interventions with a broad-based, population-wide, positive mental health promotion Campaign such as the Act-Belong-Commit campaign, could amplify these interventions\u27 impact on help-seeking by increasing openness about mental health issues

Partially integrable systems in multidimensions by a variant of the dressing method. 1

In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially integrable''. Such a construction is achieved using a suitable modification of the classical dressing scheme, consisting in assuming that the kernel of the basic integral operator of the dressing formalism be nontrivial. This new hypothesis leads to the construction of: 1) a linear system of compatible spectral problems for the solution $U(\lambda;x)$ of the integral equation in 3 independent variables each (while the usual dressing method generates spectral problems in 1 or 2 dimensions); 2) a system of nonlinear partial differential equations in $n$ dimensions ($n>3$), possessing a manifold of analytic solutions of dimension ($n-2$), which includes one largely arbitrary relation among the fields. These nonlinear equations can also contain an arbitrary forcing.Comment: 21 page