$EVWUDFW 7KH WDVN RI RXWOLHU GHWHFWLRQ LV WR ILQG VPDOO JURXSV RI GDWD REMHFWV WKDW DUH H[FHSWLRQDO ZKHQ FRPSDUHG ZLWK UHVW ODUJH DPRXQW RI GDWD 'HWHFWLRQ RI VXFK RXWOLHUV LV LPSRUWDQW IRU PDQ\ DSSOLFDWLRQV VXFK DV IUDXG GHWHFWLRQ DQG FXVWRPHU PLJUDWLRQ 0RVW VXFK DSSOLFDWLRQV DUH KLJK GLPHQVLRQDO GRPDLQV LQ ZKLFK WKH GDWD PD\ FRQWDLQ KXQGUHGV RI GLPHQVLRQV +RZHYHU WKH RXWOLHU GHWHFWLRQ SUREOHP ...

In this paper the regularity of weak solutions and the blow-up criteria of smooth solutions to the micropolar fluid equations on three dimension space are studied in the Lorentz space L(R). We obtain that if u ∈ Lq(0, T ;L(R)) for 2 q + 3 p ≤ 1 with 3 < p ≤ ∞; or ∇u ∈ Lq(0, T ;L(R)) for 2 q + 3 p ≤ 2 with 3 2 < p ≤ ∞; or the pressure P ∈ Lq(0, T ;L(R)) for 2 q + 3 p ≤ 2 with 3 2 < p ≤ ∞; or ∇P ...

We introduce a new variant of the number field sieve algorithm for discrete logarithms in Fpn called exTNFS. The most important modification is done in the polynomial selection step, which determines the cost of the whole algorithm: if one knows how to select good polynomials to tackle discrete logarithms in Fpκ , exTNFS allows to use this method when tackling Fpηκ whenever gcd(η, κ) = 1. This ...

Here θ is a probability measure on a Polish space , Dr k k = 1 2r is a dyadic partition of (hence the use of 2r summands) satisfying θ Dr k = 1/2r and Lq 1 Lq 2 Lq 2r is an independent, identically distributed sequence of random probability measures on a Polish space such that Lq k q ∈ N satisfies the large deviation principle with a convex rate function. A number of related asymptotic results ...

9DULRXV HOHFWURQLF PHHWLQJ VXSSRUW V\VWHPV KDYH EHHQ VWXGLHG DQG GHYHORSHG 7KRXJK FRPSXWDWLRQDO DVSHFW RI VXFK V\VWHPV H J V\VWHP SHUIRUPDQFH 2NDGD RU WKHLU LPSDFW LQ EXVLQHVV RIILFHV KDYH EHHQ GLVFXVVHG H[WHQVLYHO\ WKH FXOWXUDO DVSHFW HVSHFLDOO\ LQ WKH FDVHV ZKHUH SHRSOH IURP KHWHURJHQHRXV FXOWXUHV LQWHUDFW ZLWK HDFK RWKHU KDYH QRW EHHQ H[DPLQHG HQRXJK 6XSSRVH VXFK V\VWHPV WKDW VXSSRUW LQWHUQD...

We study some relation between some geometrically defined classes of diffeomorphisms between manifolds and the Lq,p-cohomology of these manifolds. Some applications to vanishing and non vanishing results in Lq,pcohomology are given.

$EVWUDFW ,Q WKLV SDSHU ZH UHSRUW RQ WKH UHVXOWV RI SHUIRUPDQFH PHDVXUHPHQWV IRU DQ LQWHJUDWHG % ,6'1 ,QWHOOLJHQW 1HWZRUN VLJQDOLQJ QHWZRUN 7KH VSHFLILFDWLRQ LPSOHPHQWDWLRQ DQG UHDOL]DWLRQ DV ZHOO DV WKH SHUIRUPDQFH PHDVXUHPHQWV DUH DOO SDUW RI D (XURSHDQ SURMHFW QDPHG ,16,*1,$ 7KH UHVXOWV UHSRUWHG LQ WKLV SDSHU SHUWDLQ WR WKH VLJQDOLQJ V\VWHP EXLOW LQ WKH VHFRQG WULDO RI WKH SURMHFW DQG SHUWDLQ...

$EVWUDFW 7KH SDSHU GHVFULEHV XVDELOLW\ HYDOXDWLRQ RI D SURWRW\SH DUFKLYH LQ D SURMHFW ZKHUH 6*0/ EDVHG VROXWLRQV IRU WKH )LQQLVK 3DUOLDPHQW DQG PLQLVWULHV KDYH EHHQ GHYHORSHG DQG VWXGLHG 7KH DUFKLYH FRQVLVWHG RI WKUHH W\SHV RI SDU OLDPHQWDU\ GRFXPHQWV LQ 6*0/ IRUPDW $ XVDELOLW\ LQ VSHFWLRQ ZDV SUHFHGHG E\ DQ H[WHQVLYH DQDO\VLV RI WKH GRFXPHQW PDQDJHPHQW LQ WKH )LQQLVK OHJLVODWLYH DQG EXGJHWDU\ ...