On the Invalidity of Fourier Series Expansions of Fractional Order

The purpose of this short paper is to show the invalidity of a Fourier series expansion of fractional order as derived by G. Jumarie in a series of papers. In his work the exponential functions $e^{in\omega x}$ are replaced by the Mittag-Leffler functions $E_\alpha \left (i (n\omega x)^\alpha\right) ,$ over the interval $[0, M_\alpha/ \omega]$ where $0< \omega<\infty$ and $M_\alpha$ is the period of the function $E_\alpha \left( ix^\alpha\right),$ i.e., $E_\alpha \left( ix^\alpha\right)=E_\alpha \left( i(x+M_\alpha)^\alpha\right).

On the inversion of integral transforms associated with Sturm-Liouville problems

AbstractConsider the Sturm-Liouville boundary-value problem 1.(1) y″ − q(x) y = −t2y, −∞ < a ⩽ x ⩽ b < ∞2.(2) y(a) cos α + y′(a) sin α = 03.(3) y(b) cos β + y′(b) sin β = 0, where q(x) is continuous on [a, b]. Let φ(x, t) be a solution of either the initial-value problem (1) and (2) or (1) and (3). In this paper we develop two techniques to invert the integral F(t) = ∝abf(x) φ(x, t) dx, where f(x) ϵ L2(a, b); one technique is based on the construction of some biorthogonal sequence of functions and the other is based on Poisson's summation formula

A generalized inversion formula for the continuous Jacobi transform

In this paper we extend the definition of the continuous Jacobi transform to a class of generalized functions and obtain a generalized inversion formula for it. As a by-product of our technique we obtain a necessary and sufficient condition for an analytic function F(λ) in Reλ>0 to be the continuous Jacobi transform of a generalized function

Kristalna struktura i optička svojstva sustava Bi-Sb-Te-Se

The quaternary systems of Bi-Sb-Te-Se were synthesized by direct fusion technique. Thin films of these compounds were prepared by thermal evaporation under vacuum of 10−4 Pa. The structural properties of these compounds in powder and thin film forms were investigated by X-ray diffraction. The optical constants (absorption coefficient and band gap) of the thin films were determined by measurements of IR absorbance in the region 2.5 – 10 µm. Analysis of the optical absorption spectra revealed the existence of two direct energy gaps.Sintetizirali smo sustave Bi-Sb-Te-Se sa četiri sastavnice izravnom metodom staljivanja. Tanke slojeve tih spojeva pripremali smo isparavanjem u vakuumu (na 10−4 Pa). Primjenom rendgenske difrakcije odredili smo strukturna svojstva praha i tankih slojeva tih spojeva. Optičke konstante tankih slojeva (koeficijent apsorpcije i procijep med–u vrpcama) odredili smo mjerenjem apsorpcije u području 2.5 – 10 µm. Analiza optičkih apsorpcijskih spektara pokazuje dva izravna procijepa

The Role of Extracellular Vesicles as Modulators of the Tumor Microenvironment, Metastasis and Drug Resistance in Colorectal Cancer.

Colorectal cancer (CRC) is one of the most common cancers worldwide, with high morbidity and mortality rates. A number of factors including modulation of the tumor microenvironment, high metastatic capability, and resistance to treatment have been associated with CRC disease progression. Recent studies have documented that tumor-derived extracellular vesicles (EVs) play a significant role in intercellular communication in CRC via transfer of cargo lipids, proteins, DNA and RNAs to the recipient tumor cells. This transfer influences a number of immune-related pathways leading to activation/differentiation/expression of immune cells and modulation of the tumor microenvironment that plays a significant role in CRC progression, metastasis, and drug resistance. Furthermore, tumor-derived EVs are secreted in large amounts in biological fluids of CRC patients and as such the expression analysis of EV cargoes have been associated with prognosis or response to therapy and may be a source of therapeutic targets. This review aims to provide a comprehensive insight into the role of EVs in the modulation of the tumor microenvironment and its effects on CRC progression, metastasis, and drug resistance. On the other hand, the potential role of CRC derived EVs as a source of biomarkers of response and therapeutic targets will be discussed in detail to understand the dynamic role of EVs in CRC diagnosis, treatment, and management

Sanguinarine Induces Apoptosis Pathway in Multiple Myeloma Cell Lines via Inhibition of the JaK2/STAT3 Signaling.

Sanguinarine (SNG), a benzophenanthridine alkaloid, has displayed various anticancer abilities in several vivo and studies. However, the anticancer potential of SNG is yet to be established in multiple myeloma (MM), a mostly incurable malignancy of plasma cells. In this study, we aimed to investigate the potential anti-proliferative and pro-apoptotic activities of SNG in a panel of MM cell lines (U266, IM9, MM1S, and RPMI-8226). SNG treatment of MM cells resulted in a dose-dependent decrease in cell viability through mitochondrial membrane potential loss and activation of caspase 3, 9, and cleavage of PARP. Pre-treatment of MM cells with a universal caspase inhibitor, Z-VAD-FMK, prevented SNG mediated loss of cell viability, apoptosis, and caspase activation, confirming that SNG-mediated apoptosis is caspase-dependent. The SNG-mediated apoptosis appears to be resulted from suppression of the constitutively active STAT3 with a concomitant increase in expression of protein tyrosine phosphatase (SHP-1). SNG treatment of MM cells leads to down-regulation of the anti-apoptotic proteins including cyclin D, Bcl-2, Bclxl, and XIAP. In addition, it also upregulates pro-apoptotic protein, Bax. SNG mediated cellular DNA damage in MM cell lines by induction of oxidative stress through the generation of reactive oxygen species and depletion of glutathione. Finally, the subtoxic concentration of SNG enhanced the cytotoxic effects of anticancer drugs bortezomib (BTZ) by suppressing the viability of MM cells via induction of caspase-mediated apoptosis. Altogether our findings demonstrate that SNG induces mitochondrial and caspase-dependent apoptosis, generates oxidative stress, and suppresses MM cell lines proliferation. In addition, co-treatment of MM cell lines with sub-toxic doses of SNG and BTZ potentiated the cytotoxic activity. These results would suggest that SNG could be developed into therapeutic agent either alone or in combination with other anticancer drugs in MM

Sanguinarine Induces Apoptosis Pathway in Multiple Myeloma Cell Lines via Inhibition of the JaK2/STAT3 Signaling

Sanguinarine (SNG), a benzophenanthridine alkaloid, has displayed various anticancer abilities in several vivo and in vitro studies. However, the anticancer potential of SNG is yet to be established in multiple myeloma (MM), a mostly incurable malignancy of plasma cells. In this study, we aimed to investigate the potential anti-proliferative and pro-apoptotic activities of SNG in a panel of MM cell lines (U266, IM9, MM1S, and RPMI-8226). SNG treatment of MM cells resulted in a dose-dependent decrease in cell viability through mitochondrial membrane potential loss and activation of caspase 3, 9, and cleavage of PARP. Pre-treatment of MM cells with a universal caspase inhibitor, Z-VAD-FMK, prevented SNG mediated loss of cell viability, apoptosis, and caspase activation, confirming that SNG-mediated apoptosis is caspase-dependent. The SNG-mediated apoptosis appears to be resulted from suppression of the constitutively active STAT3 with a concomitant increase in expression of protein tyrosine phosphatase (SHP-1). SNG treatment of MM cells leads to down-regulation of the anti-apoptotic proteins including cyclin D, Bcl-2, Bclxl, and XIAP. In addition, it also upregulates pro-apoptotic protein, Bax. SNG mediated cellular DNA damage in MM cell lines by induction of oxidative stress through the generation of reactive oxygen species and depletion of glutathione. Finally, the subtoxic concentration of SNG enhanced the cytotoxic effects of anticancer drugs bortezomib (BTZ) by suppressing the viability of MM cells via induction of caspase-mediated apoptosis. Altogether our findings demonstrate that SNG induces mitochondrial and caspase-dependent apoptosis, generates oxidative stress, and suppresses MM cell lines proliferation. In addition, co-treatment of MM cell lines with sub-toxic doses of SNG and BTZ potentiated the cytotoxic activity. These results would suggest that SNG could be developed into therapeutic agent either alone or in combination with other anticancer drugs in MM

Biosynthetic potential of the global ocean microbiome

8 pages, 4 figures, supplementary information https://doi.org/10.1038/s41586-022-04862-3.-- This Article is contribution number 130 of Tara OceansNatural microbial communities are phylogenetically and metabolically diverse. In addition to underexplored organismal groups1, this diversity encompasses a rich discovery potential for ecologically and biotechnologically relevant enzymes and biochemical compounds2,3. However, studying this diversity to identify genomic pathways for the synthesis of such compounds4 and assigning them to their respective hosts remains challenging. The biosynthetic potential of microorganisms in the open ocean remains largely uncharted owing to limitations in the analysis of genome-resolved data at the global scale. Here we investigated the diversity and novelty of biosynthetic gene clusters in the ocean by integrating around 10,000 microbial genomes from cultivated and single cells with more than 25,000 newly reconstructed draft genomes from more than 1,000 seawater samples. These efforts revealed approximately 40,000 putative mostly new biosynthetic gene clusters, several of which were found in previously unsuspected phylogenetic groups. Among these groups, we identified a lineage rich in biosynthetic gene clusters (‘Candidatus Eudoremicrobiaceae’) that belongs to an uncultivated bacterial phylum and includes some of the most biosynthetically diverse microorganisms in this environment. From these, we characterized the phospeptin and pythonamide pathways, revealing cases of unusual bioactive compound structure and enzymology, respectively. Together, this research demonstrates how microbiomics-driven strategies can enable the investigation of previously undescribed enzymes and natural products in underexplored microbial groups and environmentsThis work was supported by funding from the ETH and the Helmut Horten Foundation; the Swiss National Science Foundation (SNSF) through project grants 205321_184955 to S.S., 205320_185077 to J.P. and the NCCR Microbiomes (51NF40_180575) to S.S.; by the Gordon and Betty Moore Foundation (https://doi.org/10.37807/GBMF9204) and the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 101000392 (MARBLES) to J.P.; by an ETH research grant ETH-21 18-2 to J.P.; and by the Peter and Traudl Engelhorn Foundation and by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 897571 to C.C.F. S.L.R. was supported by an ETH Zurich postdoctoral fellowship 20-1 FEL-07. M.L., L.M.C. and G.Z. were supported by EMBL Core Funding and the German Research Foundation (DFG, Deutsche Forschungsgemeinschaft, project no. 395357507, SFB 1371 to G.Z.). M.B.S. was supported by the NSF grant OCE#1829831. C.B. was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement Diatomic, no. 835067). S.G.A. was supported by the Spanish Ministry of Economy and Competitiveness (PID2020-116489RB-I00). M.K. and H.M. were funded by the SNSF grant 407540_167331 as part of the Swiss National Research Programme 75 ‘Big Data’. M.K., H.M. and A.K. are also partially funded by ETH core funding (to G. Rätsch)With the institutional support of the ‘Severo Ochoa Centre of Excellence’ accreditation (CEX2019-000928-S)Peer reviewe