The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generali...The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .展开更多
Raynaud’s phenomenon is a symptom complex manifested as intermittent fingertip ischemia caused by cold or other sympathetic drivers.Secondary Raynaud’s phenomenon is often more severe and could even lead to finger u...Raynaud’s phenomenon is a symptom complex manifested as intermittent fingertip ischemia caused by cold or other sympathetic drivers.Secondary Raynaud’s phenomenon is often more severe and could even lead to finger ulceration,making it particularly complicated to treat.We describe a case of severe Raynaud’s phenomenon secondary to subclinical hypothyroidism lasting for more than 6 hours in a 65-year-old woman.The patient was also diagnosed with hypothyroidism,epilepsy,and secondary soft tissue infection of the right middle and ring fingers.After careful multidisciplinary consultation and discussion,the patient received vasodilation,anticoagulation,thyroxine supplementation,stellate ganglion block,hyperbaric oxygen therapy and debridement.The patient responded well to the medication,avoiding amputation or obviously dysfunction.Multidisciplinary team gathering the doctors from different departments proposes appropriate strategies for patients with severe Raynaud’s phenomenon and could improve the prognosis and satisfaction of patient effectively.展开更多
This article deals with the problem of calculating the comparative uncertainty of the main variable in the model of the studied physical phenomenon, which depends on a qualitative and quantitative set of variables. Th...This article deals with the problem of calculating the comparative uncertainty of the main variable in the model of the studied physical phenomenon, which depends on a qualitative and quantitative set of variables. The choice of variables is determined by preliminary information available to the observer and dependent on his knowledge, experience and intuition. The finite value of the amount of information available to the researcher leads to the inevitable aberration of the observed object. This causes the existence of an unremovable and intractable processing by any statistical methods, a comparative (respectively, relative) uncertainty of the model. The goal is to present a theoretical justification for the existence of this uncertainty and proposes a procedure for its calculation. The practical application of the informational method for choosing the preferred model for the Einstein formula and for calculating the speed of sound is demonstrated.展开更多
文摘The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .
文摘Raynaud’s phenomenon is a symptom complex manifested as intermittent fingertip ischemia caused by cold or other sympathetic drivers.Secondary Raynaud’s phenomenon is often more severe and could even lead to finger ulceration,making it particularly complicated to treat.We describe a case of severe Raynaud’s phenomenon secondary to subclinical hypothyroidism lasting for more than 6 hours in a 65-year-old woman.The patient was also diagnosed with hypothyroidism,epilepsy,and secondary soft tissue infection of the right middle and ring fingers.After careful multidisciplinary consultation and discussion,the patient received vasodilation,anticoagulation,thyroxine supplementation,stellate ganglion block,hyperbaric oxygen therapy and debridement.The patient responded well to the medication,avoiding amputation or obviously dysfunction.Multidisciplinary team gathering the doctors from different departments proposes appropriate strategies for patients with severe Raynaud’s phenomenon and could improve the prognosis and satisfaction of patient effectively.
文摘This article deals with the problem of calculating the comparative uncertainty of the main variable in the model of the studied physical phenomenon, which depends on a qualitative and quantitative set of variables. The choice of variables is determined by preliminary information available to the observer and dependent on his knowledge, experience and intuition. The finite value of the amount of information available to the researcher leads to the inevitable aberration of the observed object. This causes the existence of an unremovable and intractable processing by any statistical methods, a comparative (respectively, relative) uncertainty of the model. The goal is to present a theoretical justification for the existence of this uncertainty and proposes a procedure for its calculation. The practical application of the informational method for choosing the preferred model for the Einstein formula and for calculating the speed of sound is demonstrated.
