HPN Associates
HPN may refer to: * Hapton railway station, England * Higgs prime, Hp_n * HPN (gene) * Quaternionic projective space, \mathbb\mathrm^n * Westchester County Airport Westchester County Airport is a county-owned airport in Westchester County, New York, Westchester County, New York (state), New York, United States, northeast of downtown White Plains, New York, White Plains, with territory in the Town (New Y ...

Hapton Railway Station
Hapton railway station serves the village of Hapton west of Burnley Central railway station on the East Lancashire Line operated by Northern Trains. It is unstaffed. Between 2004–5 and 2005–6, passenger usage fell by 21%, but in the years since, it has risen again by more than 60%. The station has only basic facilities available, the standard plexiglass shelters, passenger information screens and PA system, with no permanent buildings. It is fully accessible for disabled travellers, via ramps from the nearby main road to each platform. Services Monday to Saturday, there is an hourly service from Hapton to Burnley and Colne (eastbound) and Preston via Accrington and Blackburn (westbound). On Sundays, there is a two-hourly service in each direction, with through running to and from . On 14 May 2012, Hapton became a request only stop, along with Huncoat, Burnley Barracks and Pleasington Pleasington () is a village and civil parish in the Borough of Blackburn with Da ...
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Higgs Prime
A Higgs prime, named after Denis Higgs, is a prime number with a totient (one less than the prime) that evenly divides the square of the product of the smaller Higgs primes. (This can be generalized to cubes, fourth powers, etc.) To put it algebraically, given an exponent ''a'', a Higgs prime ''Hp''''n'' satisfies : \phi(Hp_n), \prod_^ ^a\mboxHp_n > Hp_ where Φ(''x'') is Euler's totient function. For squares, the first few Higgs primes are 2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 43, 47, ... . So, for example, 13 is a Higgs prime because the square of the product of the smaller Higgs primes is 5336100, and divided by 12 this is 444675. But 17 is not a Higgs prime because the square of the product of the smaller primes is 901800900, which leaves a remainder of 4 when divided by 16. From observation of the first few Higgs primes for squares through seventh powers, it would seem more compact to list those primes that are not Higgs primes: Observation further revea ...
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HPN (gene)
Serine protease hepsin is an enzyme that in humans is encoded by the ''HPN'' gene. Function Hepsin is a cell surface serine protease. Hepson contains a peptidase S1 domain and an SRCR domain. The SRCR domain is located in the extracellular part of the protein, it is formed primarily by three elements of regular secondary structure: a 12-residue alpha helix, a twisted five-stranded antiparallel beta sheet, and a second, two-stranded, antiparallel sheet. The two beta-sheets lie at roughly right angles to each other, with the helix nestled between the two, adopting an SRCR fold. The exact function of this domain has not been identified, though it probably may serve to orient the protease domain or place it in the vicinity of its substrate. Clinical significance Hepsin expression is unregulated in prostate cancer Prostate cancer is the neoplasm, uncontrolled growth of cells in the prostate, a gland in the male reproductive system below the bladder. Abnormal growth of the ...
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Quaternionic Projective Space
In mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates lie in the ring of quaternions \mathbb. Quaternionic projective space of dimension ''n'' is usually denoted by :\mathbb^n and is a closed manifold of (real) dimension 4''n''. It is a homogeneous space for a Lie group action, in more than one way. The quaternionic projective line \mathbb^1 is homeomorphic to the 4-sphere. In coordinates Its direct construction is as a special case of the projective space over a division algebra. The homogeneous coordinates of a point can be written : _0,q_1,\ldots,q_n/math> where the q_i are quaternions, not all zero. Two sets of coordinates represent the same point if they are 'proportional' by a left multiplication by a non-zero quaternion ''c''; that is, we identify all the : q_0,cq_1\ldots,cq_n/math>. In the language of group actions, \mathbb^n is the orbit space of \mathbb^\setminu ...
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