Abstract In this paper, the deformation of special relativity within the frame of conformable derivative is formulated. Within this context, the two postulates of the theory are re-stated. Then, the addition of velocity laws are derived and used to verify the constancy of the speed of light. The invariance principle of the laws of physics is demonstrated for some typical illustrative examples, namely, the conformable wave equation, the conformable Schrodinger equation, the conformable Klein-Gordon equation, and conformable Dirac equation. The current formalism may be applicable when using special relativity in a nonlinear or dispersive medium.

A new spectral continuous wavelet transform (CWT) methods are proposed for the quantitative analysis of the binary mixtures. The simultaneous spectral resolution of binary mixtures and tablets containing paracetamol (PAR) and chloroxozone (CHL) with overlapping absorption spectra is performed by six wavelet families with no chemical separation procedure. The calibration graphs for the six wavelet families are obtained by the help of the data collected from the CWT- signal amplitudes corresponding to the zero crossing points inthe spectral range of 210 nm-310nm. The validation of each wavelet family is carriedoutby analyzing various synthetic binary mixtures of the above mentioned drugs. The second derivative spectrophotometry (D2) is used to compare the experimental results provided by the analyzed continuous wavelet families and a good coincidence is reported for the proposed analytical approaches.

Signal processing methods based on the combined use of the continuous wavelet transform (CWT) and zero-crossing technique were applied to the simultaneous spectrophotometric determination of perindopril (PER) and indapamide (IND) in tablets. These signal processing methods do not require any priory separation step. Initially, various wavelet families were tested to identify the optimum signal processing giving the best recovery results. From this procedure, the Haar and Biorthogonal1.5 continuous wavelet transform (HAAR-CWT and BIOR1.5-CWT, respectively) were found suitable for the analysis of the related compounds. After transformation of the absorbance vectors by using HAAR-CWT and BIOR1.5-CWT, the CWT-coefficients were drawn as a graph versus wavelength and then the HAAR-CWT and BIOR1.5-CWT spectra were obtained. Calibration graphs for PER and IND were obtained by measuring the CWT amplitudes at 231.1 and 291.0 nm in the HAAR-CWT spectra and at 228.5 and 246.8 nm in BIOR1.5-CWT spectra, respectively. In order to compare the performance of HAAR-CWT and BIOR1.5-CWT approaches, derivative spectrophotometric (DS) method and HPLC as comparison methods, were applied to the PER-IND samples. In this DS method, first derivative absorbance values at 221.6 for PER and 282.7 nm for IND were used to obtain the calibration graphs. The validation of the CWT and DS signal processing methods was carried out by using the recovery study and standard addition technique. In the following step, these methods were successfully applied to the commercial tablets containing PER and IND compounds and good accuracy and precision were reported for the experimental results obtained by all proposed signal processing methods.

A determinação simultânea de ácido ascórbico (AA), ácido acetilsalicílico (ASP) e paracetamol (PAR) em misturas sintéticas e tabletes efervescentes foi realizada usando-se as técnicas de transformações de Haar e transformações de onda pequena tipo chapéu mexicano (HAAR-CWT e MEXH-CWT, respectivamente), juntamente com a técnica de divisor duplo. Os métodos de processamento de sinal são baseados na aplicação de HAAR-CWT e MEXH-CWT aos espectros relativos com divisor duplo (DDRS). Estes espectros foram obtidos pela divisão do espectro de absorção do composto puro e suas misturas ternárias, por um divisor duplo ou espectro padrão correspondente à mistura de dois compostos em mistura ternária. O uso combinado de HAAR-CWT e MEXH-CWT com espectros relativos com divisor duplo (DDRS) foi denominado DDRS-HAAR CWT e DDRS-MEXH CWT. Para avaliar a habilidade ou aplicabilidade dos métodos desenvolvidos DDRS-CWT, foi aplicado como comparação, o método espectrofotométrico por derivada de espectros relativos com divisor duplo (DDRS-DS), às amostras mencionadas acima, contendo AA, ASP e PAR. Resultados satisfatórios foram obtidos.

Simultaneous determination of ascorbic acid (AA), acetylsalicylic acid (ASP) and paracetamol (PAR) in their synthetic mixtures and effervescent tablets were performed by Haar and Mexican continuous wavelet transforms (HAAR-CWT and MEXH-CWT, respectively) together with double divisor technique. The signal processing methods are based on the application of HAAR-CWT and MEXH-CWT to the double divisor-ratio spectra (DDRS). These spectra were obtained by dividing the absorption spectra of pure compound and its ternary mixtures by a double-divisor or standard spectrum corresponding to a mixture of two compounds in ternary mixture. A combined use of HAAR-CWT and MEXH-CWT with double divisor-ratio spectra (DDRS) was denoted by DDRS-HAAR CWT and DDRS-MEXH CWT. To check the ability or applicability of the developed DDRS-CWT methods, the double divisor-ratio spectra-derivative spectrophotometric (DDRS-DS) method, as a comparison method, was applied to the above mentioned samples containing AA, ASP and PAR and satisfactory results were obtained.

A resolução quantitativa da mistura de quinapril e hidroclorotiazida em comprimidos foi realizada com o uso da transformada de ondas contínuas e métodos quimiométricos. No caso da transformada de ondas contínuas, uma série de famílias de ondas foram testadas para achar o ponto ótimo da técnica de processamento de sinais das ondas. A função de onda tipo chapéu mexicano apresentou o melhor resultado. Essa função onda tipo chapéu mexicano foi aplicada aos espectros de absorção do quinapril e da hidroxiclorotiazida na faixa de 200-320 nm para um conjunto padrão de medicamentos na concentração de quinapril de 4,0-20,0 µg mL-1 e hidroclorotiazida de 2,5-12,5 µg mL-1. As funções de calibração do quinapril em 230,6 nm e da hidroclorotiazida em 271,1 nm foram calculadas em função da relação entre as medidas dos sinais de ondas contínuas e das concentrações. De acordo com o enfoque quimiométrico, foram utilizadas calibrações por regressão dos mínimos quadrados e dos componentes principais, baseadas em um conjunto de teste de 21 misturas, contendo os dois medicamentos e os dados de absorbância correspondentes, na faixa de comprimento de onda igual a 205-290 nm. Todos os métodos propostos foram validados pela análise separada das misturas sintéticas e pela técnica de adição padrão. A utilização do método desenvolvido indicou que a seletividade e a sensibilidade foram satisfatórias na análise dos comprimidos.

Quantitative resolution of the quinapril and hydrochlorothiazide mixture in tablets was achieved by using continuous wavelet transform and chemometric methods. In the case of the continuous wavelet transform, various continuous wavelet families were tested in order to find the optimum point of the wavelet signal processing technique. The Mexican hat wavelet function was reported to be the optimal one. The Mexican hat wavelet function was applied to the absorption spectra of quinapril and hydrochlorothiazide in the spectral range of 200-320 nm for standard series of drugs in the concentration range of 4.0-20.0 µg mL-1 quinapril and 2.5-12.5 µg mL-1 hydrochlorothiazide. The calibration functions for quinapril at 230.6 nm and for hydrochlorothiazide at 271.1 nm were calculated based on the relationship between the measurements of continuous wavelet signals and their concentrations. According to the chemometric approach, partial least squares and principal component regression calibrations were constructed by a training set of 21 mixtures, containing two drugs and their corresponding absorbance data, in the wavelength range of 205-290 nm. All proposed methods were validated by the independent analysis of the synthetic mixtures and by the standard addition technique. The application of the methods indicated that their selectivity and the sensitivity were satisfactory. The investigated methods were successfully applied to tablet analysis.