Critical States Embedded in the Continuum

We introduce a class of critical states which are embedded in the continuum (CSC) of one-dimensional optical waveguide array with one non-Hermitian defect. These states are at the verge of being fractal and have real propagation constant. They emerge at a phase transition which is driven by the imaginary refractive index of the defect waveguide and it is accompanied by a mode segregation which reveals analogies with the Dicke super -radiance. Below this point the states are extended while above they evolve to exponentially localized modes. An addition of a background gain or loss can turn these localized states to bound states in the continuum.Comment: 4.5 pages, 3 figures, 1 page of supplementary material including one figur

Response of discrete nonlinear systems with many degrees of freedom

We study the response of a large array of coupled nonlinear oscillators to parametric excitation, motivated by the growing interest in the nonlinear dynamics of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). Using a multiscale analysis, we derive an amplitude equation that captures the slow dynamics of the coupled oscillators just above the onset of parametric oscillations. The amplitude equation that we derive here from first principles exhibits a wavenumber dependent bifurcation similar in character to the behavior known to exist in fluids undergoing the Faraday wave instability. We confirm this behavior numerically and make suggestions for testing it experimentally with MEMS and NEMS resonators.Comment: Version 2 is an expanded version of the article, containing detailed steps of the derivation that were left out in version 1, but no additional result

Provisions Denying a Deduction for Illegal Expenses and Expenses of an Illegal Business Should be Repealed

The federal income tax law denies a deduction for illegal expenses, for any expense (legal or otherwise) of an illegal business that is trafficking in controlled substances, for losses incurred in an unlawful activity, and for bribes, kickbacks, and rebates connected with the Medicare or Medicaid program. In this Article, the authors first describe the current treatment of those items by the tax law. The Article next explains that the current treatment constitutes a penalty for the taxpayer whose deduction is denied, and then explores why such a penalty is bad policy and conflicts with the traditional purposes and goals of punishing wrongful behavior. The principal objection to the penalty imposed by the tax law’s denial of deductions for business and profit-oriented expenses is that the manner in which the size of the tax law’s penalty is determined is completely arbitrary and bears no relationship to the seriousness of the crime or the conditions under which it was committed. Another objection to the penalty is that it would be litigated in a civil tax suit in which the taxpayer would lack the protections and rights accorded to criminal defendants even though it constitutes a punishment for criminal behavior. The penalty is especially harsh as applied to the legal expenses of a marijuana business under a more stringent Code provision given the decriminalization of marijuana by many states. The Article also contends that the denial of a deduction for unlawful medical expenses conflicts with the principle allowing the patient a deduction for whatever treatment the patient chooses so long as it is based on a bona fide effort to deal with the illness. The authors recommend that Congress act to eliminate all of these tax penalties

Provisions Denying a Deduction for Illegal Expenses and Expenses of an Illegal Business Should Be Repealed

Currently, the tax law denies a deduction for business expenses that violate a federal or state law (but only if the state law is generally enforced). In addition, losses, including business losses, cannot be deducted if they arise out of an illegal activity. For example, medical expenses are denied a deduction if they are illegal. Kickbacks, bribes, and rebates given in connection with the Medicaid or Medicare program are nondeductible. Any expenses, legal or not, incurred in connection with the conduct of a business of selling a controlled substance that is prohibited by federal law (or by the law of the state in which the business is conducted) cannot be deducted. It is the contention of the authors that all of those provisions should be repealed and that there should be no restriction on the deductibility of an expense because of its illegality or its connection with an illegal activity. The authors will show in this Article that the current treatment is bad policy and not in accord with the traditional rationale for meting out punishment

Provisions Denying a Deduction for Illegal Expenses and Expenses of an Illegal Business Should Be Repealed

Currently, the tax law denies a deduction for business expenses that violate a federal or state law (but only if the state law is generally enforced). In addition, losses, including business losses, cannot be deducted if they arise out of an illegal activity. For example, medical expenses are denied a deduction if they are illegal. Kickbacks, bribes, and rebates given in connection with the Medicaid or Medicare program are nondeductible. Any expenses, legal or not, incurred in connection with the conduct of a business of selling a controlled substance that is prohibited by federal law (or by the law of the state in which the business is conducted) cannot be deducted. It is the contention of the authors that all of those provisions should be repealed and that there should be no restriction on the deductibility of an expense because of its illegality or its connection with an illegal activity. The authors will show in this Article that the current treatment is bad policy and not in accord with the traditional rationale for meting out punishment