Fourth Amendment Right or Fourth Amendment Wrong: INS Power after the Immigration Reform and Control Act of 1986

This Note examines the legal system\u27s scrutiny of the fourth amendment implications of INS workplace sweeps and suggests that the recent adoption of the IRCA (Immigration Reform and Control Act) and its criminal sanctions dictate the development of a higher standard for upholding the constitutionality of workplace raids. Consideration is first given to the type of INS activity which is under scrutiny in the course of a workplace sweep. Next, Part III will examine the development of case law pertaining to the current power of the INS to constitutionally conduct workplace sweeps under the fourth amendment. Part IV will then discuss the development of an appropriate standard against which workplace sweeps must be measured in determining their legality. Finally, this Note will conclude that the IRCA mandates the implementation of a standard for the issuance of an INS warrant based on a showing of probable cause equivalent to that applied in criminal law enforcement. It will further conclude that search warrants based on ethnic appearance are violative of the equal protection clause and that before a worker may be detained, an INS officer must have a reasonable suspicion, above ethnic appearance, that the person is undocumented

Continued fraction digit averages an Maclaurin's inequalities

A classical result of Khinchin says that for almost all real numbers $\alpha$, the geometric mean of the first $n$ digits $a_i(\alpha)$ in the continued fraction expansion of $\alpha$ converges to a number $K = 2.6854520\ldots$ (Khinchin's constant) as $n \to \infty$. On the other hand, for almost all $\alpha$, the arithmetic mean of the first $n$ continued fraction digits $a_i(\alpha)$ approaches infinity as $n \to \infty$. There is a sequence of refinements of the AM-GM inequality, Maclaurin's inequalities, relating the $1/k$-th powers of the $k$-th elementary symmetric means of $n$ numbers for $1 \leq k \leq n$. On the left end (when $k=n$) we have the geometric mean, and on the right end ($k=1$) we have the arithmetic mean. We analyze what happens to the means of continued fraction digits of a typical real number in the limit as one moves $f(n)$ steps away from either extreme. We prove sufficient conditions on $f(n)$ to ensure to ensure divergence when one moves $f(n)$ steps away from the arithmetic mean and convergence when one moves $f(n)$ steps away from the geometric mean. For typical $\alpha$ we conjecture the behavior for $f(n)=cn$, $0<c<1$. We also study the limiting behavior of such means for quadratic irrational $\alpha$, providing rigorous results, as well as numerically supported conjectures.Comment: 32 pages, 7 figures. Substantial additions were made to previous version, including Theorem 1.3, Section 6, and Appendix

Is the growth of the child of a smoking mother influenced by the father's prenatal exposure to tobacco? A hypothesis generating longitudinal study

OBJECTIVES: Transgenerational effects of different environmental exposures are of major interest, with rodent experiments focusing on epigenetic mechanisms. Previously, we have shown that if the study mother is a non-smoker, there is increased mean birth weight, length and body mass index (BMI) in her sons if she herself had been exposed prenatally to her mother's smoking. The aim of this study was to determine whether the prenatal smoke exposure of either parent influenced the growth of the fetus of a smoking woman, and whether any effects were dependent on the fetal sex. DESIGN: Population-based prebirth cohort study. SETTING: Avon Longitudinal Study of Parents and Children. PARTICIPANTS: Participants were residents of a geographic area with expected date of delivery between April 1991 and December 1992. Among pregnancies of mothers who smoked during pregnancy, data were available concerning maternal and paternal prenatal exposures to their own mother smoking for 3502 and 2354, respectively. PRIMARY AND SECONDARY OUTCOME MEASURES: Birth weight, length, BMI and head circumference. RESULTS: After controlling for confounders, there were no associations with birth weight, length or BMI. There was a strong adjusted association of birth head circumference among boys whose fathers had been exposed prenatally (mean difference −0.35 cm; 95% CI −0.57 to −0.14; p=0.001). There was no such association with girls (interaction p=0.006). Similar associations were found when primiparae and multiparae were analysed separately. In order to determine whether this was reflected in child development, we examined the relationships with IQ; we found that the boys born to exposed fathers had lower IQ scores on average, and that this was particularly due to the verbal component (mean difference in verbal IQ −3.65 points; 95% CI −6.60 to −0.70). CONCLUSIONS: Head size differences concerning paternal fetal exposure to smoking were unexpected and, as such, should be regarded as hypothesis generating

The emergence of 4-cycles in polynomial maps over the extended integers

Let $f(x) \in \mathbb{Z}[x]$; for each integer $\alpha$ it is interesting to consider the number of iterates $n_{\alpha}$, if possible, needed to satisfy $f^{n_{\alpha}}(\alpha) = \alpha$. The sets $\{\alpha, f(\alpha), \ldots, f^{n_{\alpha} - 1}(\alpha), \alpha\}$ generated by the iterates of $f$ are called cycles. For $\mathbb{Z}[x]$ it is known that cycles of length 1 and 2 occur, and no others. While much is known for extensions to number fields, we concentrate on extending $\mathbb{Z}$ by adjoining reciprocals of primes. Let $\mathbb{Z}[1/p_1, \ldots, 1/p_n]$ denote $\mathbb{Z}$ extended by adding in the reciprocals of the $n$ primes $p_1, \ldots, p_n$ and all their products and powers with each other and the elements of $\mathbb{Z}$. Interestingly, cycles of length 4, called 4-cycles, emerge for polynomials in $\mathbb{Z}\left[1/p_1, \ldots, 1/p_n\right][x]$ under the appropriate conditions. The problem of finding criteria under which 4-cycles emerge is equivalent to determining how often a sum of four terms is zero, where the terms are $\pm 1$ times a product of elements from the list of $n$ primes. We investigate conditions on sets of primes under which 4-cycles emerge. We characterize when 4-cycles emerge if the set has one or two primes, and (assuming a generalization of the ABC conjecture) find conditions on sets of primes guaranteed not to cause 4-cycles to emerge.Comment: 14 pages, 1 figur

Crystal structure and magnetic properties of [Fe{N(CN)2}2(MeOH)2] a 2-D layered network consisting of hydrogen-bonded 1-D chains

Journal ArticleA novel 2-D layered network structure [Fe{N(CN)2}2(MeOH)2] was synthesized and characterized by X-ray crystallography, vibrational, and magnetic susceptibility. The neutral 2-D stair-like framework consists of hydrogen-bonded infinite 1-D {Fe[N(CN)2]2} ribbons that pack in a staggered arrangement where nearest-neighboring chains are slipped a/2 relative to one another. Two methanol molecules are coordinated to the FeII center via the oxygen atoms in a trans configuration resulting in a compressed FeN4O2 octahedron. Hydrogen-bond interactions occur via N(2)...H(1)--O(1) where N(2) is the amide nitrogen atom of a nearby ribbon. The magnetic susceptibility was interpreted according to an S=2 expression which includes the Weiss constant and zero-field splitting giving g=2.04, 0=-2.0 K, and D=-1.7 K. Intrachain exchange interactions were determined from a fit to an S=2 antiferromagnetic chain model leading to g=2.04 and J/kB=0.23 K. Further interchain interaction via the hydrogen bond was determined by incorporation of a molecular-field correction term yielding J'/kB=-0.02 K indicating very weak antiferromagnetic coupling between chains

MnII(N3)2(pyrazine).A 2-D layered structure consisting of ferromagnetically coupled 1-D {Mn(U-1,1-N3)2}n chains

Journal ArticleMn(N3)2(pyz) (pyz = pyrazine) consists of ferromagnetically coupled linear chains of {Mn(N3)2}n comprised of u-1,1-azido bridges together with u-pyz ligands to afford 2-D planar layers

Structure and magnetic properties of MnII[N(CN)2]2(pyrazine). An antiferromagnet with an interpenetrating 3-D network structure

Journal ArticleMn[N(CN)2]2(pyz) (pyz = pyrazine) orders antiferromagnetically at low temperature and possesses intralayer u-NCNCN and interlayer u-pyz ligands that form a pseudo-ReO3 interpenetrating network structure

Interpenetrating three-dimensional rutile-like frameworks. Crystal structure and magnetic properties of MnII[C(CN)3]2

Journal ArticleThe interpenetrating double-density rutile-like structure and magnetic properties of MnII[C(CN)3]2 are determined

Optical properties of the cation-deficient platinum chain salt K1.75Pt(CN)4¢1.5H2O

Journal ArticleThe room-temperature polarized reflectance of a potassium-deficient platinum chain salt K1.75Pt(CN)4.1.5Hz[K0 (def)CP] has been measured in the infrared and visible. The reflectance is strongly anisotropic, with a plasma edge in the red and high reflectance in the infrared for light polarized parallel to the Pt chain axis and almost frequency-independent reflectance for the transverse polarization. Analysis of the plasma edge indicates a nearly-free-electron mass for the conduction electrons. The data show the existence of an energy gap at room temperature and suggest a Peierls transition above room temperature: The parallel polarized reflectance has structure in the infrared which is the first direct evidence for strong coupling of the conduction electrons to the C - N stretching vibration of the tetracyanoplatinate unit in quasi-one-dimensional platinum chain conductors