Rayleigh wave dispersion can occur according to complex mode excitation such that the interpretation of the phase or group velocity spectra can be erroneous thus leading to wrong reconstruction of the subsurface shear-wave velocity profile. In this paper, we present a case study solved by considering the holistic analysis of the Rayleigh waves recorded by a single three-component (3C) geophone and inverted by considering the group-velocity spectra of the radial and vertical components together with the Radial-to-Vertical Spectral Ratio (RVSR) and the RPM (Rayleigh-wave Particle Motion) frequency curve. In order to test the performance of the considered methodologies, we intentionally considered a complex site characterized by a high level of background noise and with a limited space to perform the investigation. In addition, passive data collected by the same 3C geophone are used to compute the Horizontal-to-Vertical Spectral Ratio (HVSR). Due to the vibrations produced by a nearby excavator, in order to obtain a meaningful HVSR we selected only a small portion of the recorded data. Computed HVSR is then jointly inverted with the active data to further validate the retrieved subsurface model and obtain information about the shear-wave velocities of the deeper layers. Altogether, four different inversion strategies are pursued and the obtained VS profiles compared also with the data available from local penetrometer test and borehole information.
Existence results are established for the resonant problem $y^{\prime \prime }+\lambda _m \,a\,y=f(t,y)$ a.e. on $[0,1]$ with $y$ satisfying Dirichlet boundary conditions. The problem is singular since $f$ is a Carathéodory function, $a\in L_{{\mathrm loc}}^1(0,1)$ with $a>0$ a.e. on $[0,1]$ and $\int ^1_0 x(1-x)a(x)\,\mathrm{d}x <\infty $.
We provide sufficient conditions for solvability of a singular Dirichlet boundary value problem with φ-Laplacian (φ(u ' ))' = f(t, u, u ' ), u(0) = A, u(T) = B, where φ is an increasing homeomorphism, φ(R) = R, φ(0) = 0, f satisfies the Carathéodory conditions on each set [a, b] × R 2 with [a, b] ⊂ (0, T) and f is not integrable on [0, T] for some fixed values of its phase variables. We prove the existence of a solution which has continuous first derivative on [0, T].
In this paper we present some new existence results for singular positone and semipositone boundary value problems of second order delay differential equations. Throughout our nonlinearity may be singular in its dependent variable.
Since the formal errors of many geodetic time series are also available, this paper proposes a new singular spectrum analysis (SSA) approach with stabilizing weights (SSAW) by taking the formal errors into account, where the weight of time series data is constructed based on the ratio of formal error to signal power spectrum. The formulae of the proposed SSAW are derived in detail and then used to process the real Global Mean Sea Level (GMSL) time series compared to the traditional SSA. When the first 10 principal components are used to fit the GMSL time series, the fitting errors of the SSAW and traditional SSA are 4.80 mm and 5.14 mm, with the reduction of 6.61 %. According to the 500 simulations based on the reconstructed signals and formal errors of GMSL time series, the mean root mean squared errors and mean absolute errors of reconstructed signals using the SSAW relative to traditional SSA are reduced from 2.18 mm to 1.66 mm and 1.67 mm to 1.34 mm, respectively. Therefore, if the formal errors of a noisy time series given, the proposed SSAW approach is suggested to analyze this time series.
The main purpose of this essay is critical. I focus on Robin Jeshion’s (2002; 2004; 2010) theory of singular thought, and I offer three objections to her Significance Condition for the creation of mental files. First of all, this condition makes incorrect predictions concerning singular thoughts about insignificant objects. Second, it conflicts with a theoretical aim mental file theories usually have, that of accounting for our ability to track discourse referents. And third, it appeals to a vague notion where a clear-cut notion is needed. In the final section, I suggest that there are more plausible alternatives to the Significance Condition that the mental file theorist could appeal to, and which do not face the problems mentioned., Hlavní cíl této eseje je kritický. Zaměřuji se na teorii singulární myšlenky Robina Jeshiona (2002; 2004; 2010) a nabízím tři námitky proti její podmínce významnosti pro tvorbu mentálních souborů. Především tato podmínka činí nesprávné předpovědi týkající se jednotlivých myšlenek o nevýznamných objektech. Za druhé, to je v rozporu s teoretickým cílem mentální souborové teorie obvykle mají, že účetnictví pro naši schopnost sledovat diskurz referents. A za třetí, apeluje na vágní představu, kde je zapotřebí jasného názoru. V závěrečné části navrhuji, aby existovaly více přijatelných alternativ k podmínce významnosti, na které by se mohl obrátit teoretik mentálních souborů a které by se těmto problémům nezabývaly., and Andrei Moldovan
The article offers a semantic classification of pronominal-adverb clauses expressing broad manner. The pronoun ten incorporated into the head clause most often by a secondary preposition or as a part of a multiverbation unit anticipates a subordinate clause of broad manner introduced by a pronominal relative adverb. The centre of broad-manner clauses is formed by clauses expressing narrow manner, extent or degree, means, accompanying circumstances. Clauses expressing exception and respect are close to the periphery. The periphery is formed by clauses expressing appropriate action and clauses with a relationship of attachment.