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Ghost vs WordPress

Ghost or WordPress : Which is better?

Ghost is a neat publishing focused blogging platform. Ghost allows you to write and publish your own blog, giving you the tools to make it easy and even fun to do. While WordPress works on a multi dimensional philosophy and not just limited to publishing. I was excited to try Ghost when it first released. I thought that it would be a little more nice than WordPress. But definitely, it didn’t come that strong. I am not saying that Ghost has failed to accomplish its theory. Yes it’s different and someway better than WordPress but on an a creative’s point of view it falls short to WP. (more…)

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Introducing Writ : A free Responsive WordPress Theme for writers

Writ WordPressWrit is a new & my first publicly available WordPress theme specially made for story writers, legal blogs and content based bloggers. You can download the latest version of this theme directly from Github by following this link.

 About

 Writ (noun: a piece or body of writing) is based on _s theme framework by Automattic and is aimed to be completely content focused with four optional sidebars, three in footer and one on right of the content area. It features the new WordPress post formats, featured images and custom header. As web has turned to be extremely responsive, this theme is too. Now you don’t need a separate mobile theme to display most of your content to readers. The right-aligned and left aligned (alignleft, alignright) images move right & left from main content and give pull quote effect.

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I am not the Ghost Hunter.

 

i am mohan kattimani i lived navi-mumbai. sanpada yesterday i join in ppi course and i submitted in course fees 40,000 (21-8-2014)and my scan copy. i let he no when i started  in this course.i like work in grip team. i hope future we work in together ghost hunting. my cell no {redacted}. please sir when you have time reply me.

– via my Contact Page .

Tough to understand what he really wants to say, but if you google the red words, you’ll. To ease your effort

PPI: Professional Paranormal Investigations

GRIP: Ghost Research & Investigators of Paranormal

Here GRIP TEAM is a part of Indian Paranormal Society, lead by Gaurav Tiwari , a person with the same name as mine. He’s featured on Wikipedia and Indian news resources for his work on Paranormal Theories. He is a ghost hunter. No doubt, he’s very good in that. But as Google doesn’t differentiate among persons with same name, searching ‘Gaurav Tiwari’ will mostly return my websites & social accounts in result.

This ‘accidental’ reader Mohan was tricked by the same thing. And so were the other four who contacted me for the same ‘ghost hunting training’ thing. I don’t bother about phone calls or emails they do, but I care about the time they waste for nothing good.

If it is bad to hear a caller at night who wants to talk about ghost hunting, nothing is worse than a person sending you his stories about ghosts he met. An Indore guy told me that he woke late night at 02:00 AM just to talk with me, as he knew that I lived was in U.S.A. “that time” .

Non-sense! I’ve never been to anywhere outside India, except Nepal. :-p

I am this guy and he is that guy. So, If you are a paranormal enthusiast, please make sure you contact the right people√. They live in New Delhi, not USA etc. and they are easily reachable.

 

 

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This Prime Generating Product generates successive prime factors

Any integer greater than 1 is called a prime number if and only if its positive factors are 1 and the number p itself.

The basic ideology involved in this post is flawed and the post has now been moved to Archives.

- The Editor

mistaken

via xkcd

Prime Generating Formulas

We all know how hard it is to predict a formula for prime numbers! They have extremely uncertain pattern at various number ranges. Some prime numbers may have difference of hundreds, while few others are as close as possible. Mathematicians and computer scientists have worked very well for a long time to discover more prime numbers and tried hard to compute a unique formula. But as there are no certain patterns, it remains difficult to discover exactly the next prime number after a certain prime. There are still some ideas available which help mathematics majors predict patterns in prime numbers.

 

I have already discussed two such (flawed) ideas about prime numbers generation. You can revisit them:

The third idea, originally commented by Huen Yeong Kong,  forms an accurate sequence of prime numbers. It is very extensive and appears to be true at all my computational limits. The prime factorization of product of all 2i ‘s ($i=1, 2, 3, \ldots $ ), i.e., factor ( $\displaystyle{\prod_{i=1}^n} 2i , n \in \mathbb{Z}^+$ ), gives all consecutive prime numbers in a sequence.

As an example, take $n=1$, we have $\displaystyle{\prod_{i=1}^1} 2i=2$. Therefore, $\text{factor}\prod_{i=1}^1 2i$ =2.

Similarly, for n=2, as $\displaystyle{\prod_{i=1}^2} 2i=8$, we have $\text{factor}\prod_{i=1}^2 2i$= 2.

Again, for n=3, as $\displaystyle{\prod_{i=1}^3} 2i=48$, we have $\text{factor}\prod_{i=1}^3 2i$= 2,3.

On continuing the same for different increasing values of n,  factors containing sequence of consecutive primes: 2, 3, 5, 7, 11, 13, … were obtained. The greatest (final) terms of these sequences were always less than or equal to value of chosen n.

With Maxima for Windows, a calculation beyond n=~14000 isn’t possible for this expression. For n=13000, the prime generating product $\displaystyle{\prod_{i=1}^{13000}} 2i$ was factored by writing

factor(product(2*i,i,1,100000));

in Maxima software, which yielded the following  prime factors of the number $\displaystyle{\prod_{i=1}^{13000}} 2i$:

2^25994, 3^6494, 5^3248, 7^2164, 11^1297, 13^1081, 17^810, 19^721, 23^590, 29^463, 31^432, 37^360, 41^324, 43^309, 47^281, 53^249, 59^223, 61^216, 67^196, 71^185, 73^180, 79^166, 83^157, 89^147, 97^135, 101^129, 103^127, 107^122, 109^120, 113^116, 127^102, 131^99, 137^94, 139^93, 149^87, 151^86, 157^82, 163^79, 167^77, 173^75, 179^72, 181^71, 191^68, 193^67, 197^65, 199^65, 211^61, 223^58, 227^57, 229^56, 233^55, 239^54, 241^53, 251^51, 257^50, 263^49, 269^48, 271^47, 277^46, 281^46, 283^45, 293^44, 307^42, 311^41, 313^41, 317^41, 331^39, 337^38, 347^37, 349^37, 353^36, 359^36, 367^35, 373^34, 379^34, 383^33, 389^33, 397^32, 401^32, 409^31, 419^31, 421^30, 431^30, 433^30, 439^29, 443^29, 449^28, 457^28, 461^28, 463^28, 467^27, 479^27, 487^26, 491^26, 499^26, 503^25, 509^25, 521^24, 523^24, 541^24, 547^23, 557^23, 563^23, 569^22, 571^22, 577^22, 587^22, 593^21, 599^21, 601^21, 607^21, 613^21, 617^21, 619^21, 631^20, 641^20, 643^20, 647^20, 653^19, 659^19, 661^19, 673^19, 677^19, 683^19, 691^18, 701^18, 709^18, 719^18, 727^17, 733^17, 739^17, 743^17, 751^17, 757^17, 761^17, 769^16, 773^16, 787^16, 797^16, 809^16, 811^16, 821^15, 823^15, 827^15, 829^15, 839^15, 853^15, 857^15, 859^15, 863^15, 877^14, 881^14, 883^14, 887^14, 907^14, 911^14, 919^14, 929^13, 937^13, 941^13, 947^13, 953^13, 967^13, 971^13, 977^13, 983^13, 991^13, 997^13, 1009^12, 1013^12, 1019^12, 1021^12, 1031^12, 1033^12, 1039^12, 1049^12, 1051^12, 1061^12, 1063^12, 1069^12, 1087^11, 1091^11, 1093^11, 1097^11, 1103^11, 1109^11, 1117^11, 1123^11, 1129^11, 1151^11, 1153^11, 1163^11, 1171^11, 1181^11, 1187^10, 1193^10, 1201^10, 1213^10, 1217^10, 1223^10, 1229^10, 1231^10, 1237^10, 1249^10, 1259^10, 1277^10, 1279^10, 1283^10, 1289^10, 1291^10, 1297^10, 1301^9, 1303^9, 1307^9, 1319^9, 1321^9, 1327^9, 1361^9, 1367^9, 1373^9, 1381^9, 1399^9, 1409^9, 1423^9, 1427^9, 1429^9, 1433^9, 1439^9, 1447^8, 1451^8, 1453^8, 1459^8, 1471^8, 1481^8, 1483^8, 1487^8, 1489^8, 1493^8, 1499^8, 1511^8, 1523^8, 1531^8, 1543^8, 1549^8, 1553^8, 1559^8, 1567^8, 1571^8, 1579^8, 1583^8, 1597^8, 1601^8, 1607^8, 1609^8, 1613^8, 1619^8, 1621^8, 1627^7, 1637^7, 1657^7, 1663^7, 1667^7, 1669^7, 1693^7, 1697^7, 1699^7, 1709^7, 1721^7, 1723^7, 1733^7, 1741^7, 1747^7, 1753^7, 1759^7, 1777^7, 1783^7, 1787^7, 1789^7, 1801^7, 1811^7, 1823^7, 1831^7, 1847^7, 1861^6, 1867^6, 1871^6, 1873^6, 1877^6, 1879^6, 1889^6, 1901^6, 1907^6, 1913^6, 1931^6, 1933^6, 1949^6, 1951^6, 1973^6, 1979^6, 1987^6, 1993^6, 1997^6, 1999^6, 2003^6, 2011^6, 2017^6, 2027^6, 2029^6, 2039^6, 2053^6, 2063^6, 2069^6, 2081^6, 2083^6, 2087^6, 2089^6, 2099^6, 2111^6, 2113^6, 2129^6, 2131^6, 2137^6, 2141^6, 2143^6, 2153^6, 2161^6, 2179^5, 2203^5, 2207^5, 2213^5, 2221^5, 2237^5, 2239^5, 2243^5, 2251^5, 2267^5, 2269^5, 2273^5, 2281^5, 2287^5, 2293^5, 2297^5, 2309^5, 2311^5, 2333^5, 2339^5, 2341^5, 2347^5, 2351^5, 2357^5, 2371^5, 2377^5, 2381^5, 2383^5, 2389^5, 2393^5, 2399^5, 2411^5, 2417^5, 2423^5, 2437^5, 2441^5, 2447^5, 2459^5, 2467^5, 2473^5, 2477^5, 2503^5, 2521^5, 2531^5, 2539^5, 2543^5, 2549^5, 2551^5, 2557^5, 2579^5, 2591^5, 2593^5, 2609^4, 2617^4, 2621^4, 2633^4, 2647^4, 2657^4, 2659^4, 2663^4, 2671^4, 2677^4, 2683^4, 2687^4, 2689^4, 2693^4, 2699^4, 2707^4, 2711^4, 2713^4, 2719^4, 2729^4, 2731^4, 2741^4, 2749^4, 2753^4, 2767^4, 2777^4, 2789^4, 2791^4, 2797^4, 2801^4, 2803^4, 2819^4, 2833^4, 2837^4, 2843^4, 2851^4, 2857^4, 2861^4, 2879^4, 2887^4, 2897^4, 2903^4, 2909^4, 2917^4, 2927^4, 2939^4, 2953^4, 2957^4, 2963^4, 2969^4, 2971^4, 2999^4, 3001^4, 3011^4, 3019^4, 3023^4, 3037^4, 3041^4, 3049^4, 3061^4, 3067^4, 3079^4, 3083^4, 3089^4, 3109^4, 3119^4, 3121^4, 3137^4, 3163^4, 3167^4, 3169^4, 3181^4, 3187^4, 3191^4, 3203^4, 3209^4, 3217^4, 3221^4, 3229^4, 3251^3, 3253^3, 3257^3, 3259^3, 3271^3, 3299^3, 3301^3, 3307^3, 3313^3, 3319^3, 3323^3, 3329^3, 3331^3, 3343^3, 3347^3, 3359^3, 3361^3, 3371^3, 3373^3, 3389^3, 3391^3, 3407^3, 3413^3, 3433^3, 3449^3, 3457^3, 3461^3, 3463^3, 3467^3, 3469^3, 3491^3, 3499^3, 3511^3, 3517^3, 3527^3, 3529^3, 3533^3, 3539^3, 3541^3, 3547^3, 3557^3, 3559^3, 3571^3, 3581^3, 3583^3, 3593^3, 3607^3, 3613^3, 3617^3, 3623^3, 3631^3, 3637^3, 3643^3, 3659^3, 3671^3, 3673^3, 3677^3, 3691^3, 3697^3, 3701^3, 3709^3, 3719^3, 3727^3, 3733^3, 3739^3, 3761^3, 3767^3, 3769^3, 3779^3, 3793^3, 3797^3, 3803^3, 3821^3, 3823^3, 3833^3, 3847^3, 3851^3, 3853^3, 3863^3, 3877^3, 3881^3, 3889^3, 3907^3, 3911^3, 3917^3, 3919^3, 3923^3, 3929^3, 3931^3, 3943^3, 3947^3, 3967^3, 3989^3, 4001^3, 4003^3, 4007^3, 4013^3, 4019^3, 4021^3, 4027^3, 4049^3, 4051^3, 4057^3, 4073^3, 4079^3, 4091^3, 4093^3, 4099^3, 4111^3, 4127^3, 4129^3, 4133^3, 4139^3, 4153^3, 4157^3, 4159^3, 4177^3, 4201^3, 4211^3, 4217^3, 4219^3, 4229^3, 4231^3, 4241^3, 4243^3, 4253^3, 4259^3, 4261^3, 4271^3, 4273^3, 4283^3, 4289^3, 4297^3, 4327^3, 4337^2, 4339^2, 4349^2, 4357^2, 4363^2, 4373^2, 4391^2, 4397^2, 4409^2, 4421^2, 4423^2, 4441^2, 4447^2, 4451^2, 4457^2, 4463^2, 4481^2, 4483^2, 4493^2, 4507^2, 4513^2, 4517^2, 4519^2, 4523^2, 4547^2, 4549^2, 4561^2, 4567^2, 4583^2, 4591^2, 4597^2, 4603^2, 4621^2, 4637^2, 4639^2, 4643^2, 4649^2, 4651^2, 4657^2, 4663^2, 4673^2, 4679^2, 4691^2, 4703^2, 4721^2, 4723^2, 4729^2, 4733^2, 4751^2, 4759^2, 4783^2, 4787^2, 4789^2, 4793^2, 4799^2, 4801^2, 4813^2, 4817^2, 4831^2, 4861^2, 4871^2, 4877^2, 4889^2, 4903^2, 4909^2, 4919^2, 4931^2, 4933^2, 4937^2, 4943^2, 4951^2, 4957^2, 4967^2, 4969^2, 4973^2, 4987^2, 4993^2, 4999^2, 5003^2, 5009^2, 5011^2, 5021^2, 5023^2, 5039^2, 5051^2, 5059^2, 5077^2, 5081^2, 5087^2, 5099^2, 5101^2, 5107^2, 5113^2, 5119^2, 5147^2, 5153^2, 5167^2, 5171^2, 5179^2, 5189^2, 5197^2, 5209^2, 5227^2, 5231^2, 5233^2, 5237^2, 5261^2, 5273^2, 5279^2, 5281^2, 5297^2, 5303^2, 5309^2, 5323^2, 5333^2, 5347^2, 5351^2, 5381^2, 5387^2, 5393^2, 5399^2, 5407^2, 5413^2, 5417^2, 5419^2, 5431^2, 5437^2, 5441^2, 5443^2, 5449^2, 5471^2, 5477^2, 5479^2, 5483^2, 5501^2, 5503^2, 5507^2, 5519^2, 5521^2, 5527^2, 5531^2, 5557^2, 5563^2, 5569^2, 5573^2, 5581^2, 5591^2, 5623^2, 5639^2, 5641^2, 5647^2, 5651^2, 5653^2, 5657^2, 5659^2, 5669^2, 5683^2, 5689^2, 5693^2, 5701^2, 5711^2, 5717^2, 5737^2, 5741^2, 5743^2, 5749^2, 5779^2, 5783^2, 5791^2, 5801^2, 5807^2, 5813^2, 5821^2, 5827^2, 5839^2, 5843^2, 5849^2, 5851^2, 5857^2, 5861^2, 5867^2, 5869^2, 5879^2, 5881^2, 5897^2, 5903^2, 5923^2, 5927^2, 5939^2, 5953^2, 5981^2, 5987^2, 6007^2, 6011^2, 6029^2, 6037^2, 6043^2, 6047^2, 6053^2, 6067^2, 6073^2, 6079^2, 6089^2, 6091^2, 6101^2, 6113^2, 6121^2, 6131^2, 6133^2, 6143^2, 6151^2, 6163^2, 6173^2, 6197^2, 6199^2, 6203^2, 6211^2, 6217^2, 6221^2, 6229^2, 6247^2, 6257^2, 6263^2, 6269^2, 6271^2, 6277^2, 6287^2, 6299^2, 6301^2, 6311^2, 6317^2, 6323^2, 6329^2, 6337^2, 6343^2, 6353^2, 6359^2, 6361^2, 6367^2, 6373^2, 6379^2, 6389^2, 6397^2, 6421^2, 6427^2, 6449^2, 6451^2, 6469^2, 6473^2, 6481^2, 6491^2, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007, 10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193, 10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333, 10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459, 10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531, 10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639, 10651, 10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, 10739, 10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, 10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, 10957, 10973, 10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, 11069, 11071, 11083, 11087, 11093, 11113, 11117, 11119, 11131, 11149, 11159, 11161, 11171, 11173, 11177, 11197, 11213, 11239, 11243, 11251, 11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317, 11321, 11329, 11351, 11353, 11369, 11383, 11393, 11399, 11411, 11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491, 11497, 11503, 11519, 11527, 11549, 11551, 11579, 11587, 11593, 11597, 11617, 11621, 11633, 11657, 11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731, 11743, 11777, 11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831, 11833, 11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, 11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011, 12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 12113, 12119, 12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, 12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323, 12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473, 12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553, 12569, 12577, 12583, 12589, 12601, 12611, 12613, 12619, 12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713, 12721, 12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 12829, 12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, 12941, 12953, 12959, 12967, 12973, 12979, 12983.

 

Above sequence contains each and every prime from 1 to 12985. This prime generating product may fail to produce such sequences at higher limits but still it is way better than Euler’s prime generating polynomial.

Any comments?

 

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New Google Play Store has a better and cleaner look

Recent trends in designs of Google Products shows Google’s approach towards unification. Since the launch of Google+, Google design team has been experimenting a lot with the interface of their major products. All products are now little or more based on Google+’s design, whether it’s GMail or YouTube, Chrome or Hangouts. Google Play Store has also encountered few minor overhauls recently. But today it received a bigger and noticeable update. Single items view is completely overhauled but there are no visible changes on listing pages of New Google Play Store .

 

Google Play Home

Play Store Home

Twitter Android App

Play Store Single Item View : Twitter

Android applications, games and movies now feature background images and videos just like Google+ profile pages do. Play Store’s top bar remains transparent until you completely scroll down featured image.

Games

Games

Google Play Books New

Play Books : Single Item view

Movies

Movies

Ratings

Ratings

Download counts, average ratings, genre/categories and share counts are displayed as blurb down the item’s name. Below these item description and screenshots are followed with your ratings, recent reviews and related items. Books don’t appear to enjoy the background images.

If you own an android, then you should be seeing these changes instantly. Or, if your Play Store hasn’t got such look, you need to wait more for the best Play Store ever.

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Perseids : Long Story Short

What are perseids?

Perseids are the regular and most predictable meteor shower which appear regularly every year. They are associated with Swift Tuttle comet and appear to rise from the radiant in the constellation Perseus. Swift Tuttle comet, formerly known as 109P, travels toward Earth’s part of solar system every 133 years leaving traces of perseids. It was last seen in 1992 after its discovery year 1862 AD. Next time Swift Tuttle is predicted to be seen in 2126 AD. Perseids, formed by motion of Swift Tuttle, are active from mid-July to end of August every calendar year and meet their peak shine in between 9th August to 14th August. This period produces beautiful sights for stargazers.   In 2013, the peak was seen on 12th August.  In 2014 too, they are expected to shine most visibly around 11-12th August. Perseids appear and disappear from human being’s achievement at a height of about 50 miles from the Earth surface.

Perseids vs Full Moon (supermoon)

As 10th August had full moon and perseids are appearing in the same period, it would be interesting how sky will look this time. Science at NASA has an illustrative analysis of this event, last time happened similarly in 2011.

The meteor showers of  2012 and 2013 were recorded in these time lapse YouTube videos:

 

 

 

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A Possible Proof of Collatz Conjecture

Our reader Eswar Chellappa has sent his work on the solution of ‘3X+1′ problem, also called Collatz Conjecture. He had been working on the proof of Collatz Conjecture off and on for almost ten years. The Collatz Conjecture can be quoted as follow:

Let $\phi : \mathbb{N} \to \mathbb{N}^+$ be a function defined  such that:
$$\phi(x):= \begin{cases} \frac{x}{2}, & \text{if } x \text{ is even } \\ 3x+1, & \text{ if } x \text{ is odd} \end{cases}$$

Then the iterates of $\phi(x)$ will eventually reach $1$ for any initial value of $x$.

See this post about Collatz Conjecture for more details.

 Plenty of proof attempts were made by various mathematicians. But none of those could flawlessly prove the statement. Mr. Chellappa’s attempt is based upon the famous Sieve of Eratosthenes. Despite of his experience & confidence, I can not guarantee if this work is perfect. I invite readers to cross check the flawlessness and tell what they think.

 

Introduction

Let, $f(x) = x/2$ if $x$ is even and  $g(x) = 3x + 1$ if $x$ is odd. Since $3x+1$ is an even number for any odd $x$, we can replace any odd number by an even number which equals to $3x+1$. And when, $3x+1$ is an even number, we can successfully halve it according to first step of the function defined in the conjecture.

The method proposed below is similar to the famous Sieve of Eratosthenes

To start with the proof, choose the natural numbers from 1 to 100.

Since we have $$f(x) = x/2$$ for even $x$. Let’s strike out all even numbers for each of them reduces to another odd or even number (less than x) by f(x), by exactly one iteration. This we do from 100 to 2, in the decreasing order.

  • We strike out 100 as $f(x)$ reduces it to 50.
  • Then we strike out 98 keeping 49 as the result of one iteration.
  • 50 is also struck out giving 25 as result of one iteration.

Now all it remains, the odd numbers and natural number $1$. As $1$ automatically verifies the conjecture, we start from 3 and end to 99.

  • We have $g(3) := 10$. Since $10$ has already been struck out, we can simply say that $3$ satisfies the conjecture. Hence we strike out 3.
  • $g(5) := 16$, so 5 can also be struck out.

By this process we can strike out all odd numbers up to 33 as we have taken only numbers up to 100 and $g(35) >100$.

By suitably increasing the range of numbers we can conclude that ultimately $\phi (x)$ has to reach 1 irrespective of the starting natural number $x$.

Any possible worries?

The only possibility that might worry us was falling in to a loop. This happens only if $\phi_i(x) = \phi_j(x) \neq 1$ where $i\neq j$. But that is not possible since $\phi (x)=x/2$ is one to one.

Remark

  • By striking out the numbers, we verify that they have images under $f(x)$. That is to say, more iterations are possible until the sequence reaches $1$.
  • Concerned about $\mathbb{N}^+$ notation?

 

PS: This isn’t a paper.

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8 big online communities a math major should join

Online communities are the groups of web savvy individuals who share communal interests. A community can be developed with just a single topic or by a bunch of philosophies. A better community binds its members through substantial debates. Mathematics is a very popular communal interest and there are hundreds of online communities formed in both Q&A and debate styles. Some mathematical communities are so immense that they serve two or three discussions every minute. If you are a math student, reader or research scholar then you must join in such places. Beyond sharpening math skills, these communities also help users to connect with other similar minded people. The following 8 communities are largest on the internet and are always worth joining:

1.Mathematics Stack Exchange

Stack Exchange is world’s largest Q&A network and the Mathematics community of this network is considered to be one of the most reliable resources for mathematics related information. Mathematics Stack Exchange is a website dedicated to all types of mathematical discussions. You can ask questions, provide answers and communicate with other users publicly.

 

Members: 166k

Since: 2010

Ideal for: Any math major

 

2. Mathematics Google+ Community

Like the fasted growing social network Google+, Mathematics Google+ community has gained an amazing crowd of over 128 thousands readers in just two years. It supports serious discussions, informative readings, blog articles and multimedia images about math & related sciences.

Members: 128k

Since: 2012

Ideal for: Any math major.

3. r/math

r/math is probably the wisest sub-reddit of reddit.com. Here you can ask questions and discuss on mathematical internet links.

Members: 118k

Since: 2008

Ideal for: Any math major.

 

4. MathOverflow

The MathOverflow is similar to Math.SE in theory, but it allows discussions about serious research topics only.

Members: 56k

Since: September 2009

Ideal for: Math graduates, research scholars

 

 

5. Math Help Forum

A forum dedicated to elementary & recreational mathematics topics.

Members: 10k

Since: 2005

Ideal for: High Schoolers, Laymen, Teens.

6. Number Theory LinkedIn Group

Open discussions about theories and new developments in number theory.

View the Number Theory Group

Members: 3.5K

Since: June 2012

Ideal for: Number Theory majors

 

7. Mathematicians LinkedIn Group

The basic idea of this community is to bring all the logical brains together and ignite the thought process of learning and teaching Mathematics with all possible practicalities.

View the community!

Members: 3.1k

Since: September 2008

Ideal for: All math majors.

 

8. PlanetMath

Planet Math

Members: 2k

Since: 2013 (current form)

PlanetMath aims to help make mathematical knowledge more accessible. The content is created collaboratively: almost the same way Wikipedia works.

Last, and the least

Question Hub header

I launched my own Q&A community, Question HUB in March 2014 for private beta and moved all Q&A based articles from the blog to the hub. Now it is open for public beta since 25th July 2014. Question HUB is hosted on gauravtiwari.org and is dedicated primarily to career & education topics, mathematics and WordPress. If you feel interested in joining the HUB, you can register here for free. You will receive your login & password once your account is approved.

QUESTION HUB!
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New Math Series: Selected Topics in Functional Analysis

This series of study notes is aimed for post-graduate (M.A/M.Sc.) students of Indian & international universities. The study of functional analysis can be started after basic topology and set theory courses. In this introductory article we will start with some elementary yet important definitions and notations from analysis. We will finish this article with the definition of Norm & Normed Linear spaces derivedfrom the notions of linear spaces. An elementary treatise of examples and their completeness of Normed (linear) Spaces will be done in upcoming articles. Using this we shall define complete normed spaces or Banach Spaces. After basic ideas are attained about Normed & Banach spaces, there will be rigorous discussion on their subspaces, quotient spaces. A relevant analysis of properties like joint continuity of addition and vector multiplication, equivalent norms, compactness, boundedness etc. will be done at last.

Topic suggestions, improvement tips and further queries are welcome through comment form or via e-mail.

CHECK OUT THE LIST OF NOTATIONS USED IN MATH ARTICLES ON MY MAGAZINE

Linear Space or Vector Space over a field K

Definition: The linear space over a field K is a non-empty set along with a function $+ : X \times X \to X$ called linear/vector addition  (or just, ‘addition‘) and another function $ \cdot : K \times X \to X$ called scalar multiplication, such that for all elements $x, y, z, \ldots$ in $X$ and $1, k, l, \ldots$ in $K$ :

$x+y = y+x$
$x+(y+z) = (x+y)+z$
there exists $0 \in X$ such that $x+0=x$
there exists $-x \in X$ such that $x+(-x)=0$
$k \cdot (x+y)=k \cdot x+k \cdot y$
$(k+l) \cdot x = k \cdot x + l \cdot x$
$(kl) \cdot x = k \cdot (l \cdot x)$
$1 \cdot x =x$

Set-Set, Set Element Summation & Products

Let small Roman letters like $x, y, a, b, \ldots$ represent the elements & capital letters like $A, B, X, Y, \ldots$ represent sets, then

  • $x+F = \{ x+y : y \in F \} $
  • $ E+F= \{ x+y: x \in E, \, y \in F \}$
  • $kE= \{ kx : x \in E \}$
  • $E \times F = \{ (x,y) : x \in E, \, y \in F \}$

Convex Subset of a linear space

A subset E of a linear space X over field K is said to be convex if $rx+(1-r)y \in E$ when $x,y \in E$ and $0<r<1$

Convex Hull of a subset of linear space

For $E \subset X$, the smallest convex subset of linear space X containing $E$ is called the convex hull of $E$, denoted by co(E).

co(E)= $ \{ \displaystyle{\sum_{i=1}^n} r_i x_i : x_i \in E; r_i \ge 0; \displaystyle{\sum_{i=1}^n} r_i=1\}$

Subspace of a linear space

A non-empty subset $Y$ of linear space $X$ over K is said to be a subspace of $X$ over K if $kx+ly \in Y$, whenever $x,y \in Y$ & $k,l \in K$.

Span of a subset of linear space

For a non-empty subset E of linear space X over K, the smallest subspace of X containing E is span(E) defined as

span(E) = $ \{ \displaystyle{\sum_{i=1}^n} k_i x_i : x_i \in E; k_i \in K \}$

This set is called the span of E.

REMARK: When span(E)=X , then we say that E spans X. Also, if span(E)=X and is a linearly independent set, E is called the Hamel Basis (or basis) of linear space X.

Linear Map

Let X and Y be two linear spaces over K. A linear map from X to Y is a function F : X →Y such that $F(k_1 x_1 + k_2 x_2) = k_1 F(x_1)+ k_2 F(x_2)$ for all $x_1, x_2 \in X, k_1, k_2 \in K$

The subspace $$ R(F):= \{ y \in Y : F(x)=y \, \mathbf{for \, some} \, x \in X \} $$ of Y is called the range space of F. While, the subspace $$ Z(F) := \{ x \in X : F(x) = 0 \}$$ of X is called the zero space of F.

REMARK:

  • Whenever Z(F)=X, we write F=0.
  • dim X= dim R + dim Z

 

Norm

Let X be a linear space over the field K of real or complex numbers. A norm on X is the function $|| \, || : X \to R$ such that for all $x, y \in X$ and $k \in K$,

  • $||x|| \ge 0$ with $||x||=0$ if and only if $x=0$
  • $||x+y|| \le ||x||+||y||$
  • $||kx|| = |k| ||x||$ where $|k|$ is the modulus of $k$.

A normed space X is a linear space with a norm ||  || on it.

Examples of Normed Space

A descriptive analysis of following normed spaces will be done in next article:

  • Spaces $\mathbb{R}^n$ and $\mathbb{C}^n$
  • Sequence spaces $l^p, l^\infty, c, c_0, c_{00}$ where $1\le p <\infty$
  • p-integrable function spaces $L^p, L^\infty$ where $1\le p <\infty$

 

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Effective PHP Scripts to use for your WordPress blog

useful php scripts

WordPress plugins are effective and easier to use. They do what they are meant to. WordPress Plugins are also built using PHP, a coding environment on which WordPress is based upon. You can get WP plugins for almost any tweak you want to do with your site. But there are still a few tweaks which can’t be done by plugins. Or, if they can be done — plugins will definitely take more load than usual. To solve this, you can always place some PHP scripts which run into your WordPress’ site’s front-end to offer wanted results. This process doesn’t need installation of plugins and hence strengthens your site’s security and keep bloats away.

This article was brought to you by Intellipaat, the team behind an awesome Hadoop developer program. You can explore the provided hyperlinks for more details!

Here is the list of some highly useful PHP scripts to use for your WordPress blog. This list is expendable and will surely expand to larger number of scripts as time moves on. All the codes listed below are error-proof and tested by me on my blogs.

Batch remove all featured images from your WordPress posts and pages

Place the given PHP code in between <?php and ?> inside your theme’s functions.php file. If there is no ending ?>, it is recommended to place the code at the end-part of the file.

 global $wpdb;
 $wpdb->query( "
 DELETE FROM $wpdb->postmeta
 WHERE meta_key = '_thumbnail_id'
 " );

After you finished placing the code, save and update the functions.php file. Viola! You see that all featured images are gone. Now you can remove above php code from functions.php as it is just a one time job. Please note that you will not be able to set featured images until you remove the mentioned code.

(more…)

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WP Rocket gives a performance dose to WordPress blogs

As a professional WordPress blogger, you start afresh. As the time and experience increase, feature demand is increased too. This costs adding new scripts to your site and makes your site heavy… and heavier. After a certain time you realize that you have made your site a garbage bin by unordered input of scripts and plugins. If you are at a fast loading CDN service or host, number of script files won’t bother you. But if you are using a comparatively slow web-host (like GoDaddy!), then you surely need a great caching plugin.

Earlier on the blog post “Make your WordPress site load faster without paying anything“, I talked smartly on how to boost the traffic load time. I felt smart after the great response the article received from my readers. I was satisfied about the page-speed my blog was getting. With W3 Total Cache, 5.89 seconds was the average page load time for the front page with almost no images and tens of scripts.  I had accepted the fact that this was the maximum optimization and the least load time possible. But my concerns about internal pages rose after I submitted the same article to Reddit and a user CTRL-Z commented this:

wow that took a good minute to load. lol.

The page loading speed per second was not impressive. First it took a lot of time connect to the servers of my CDN (cloudflare) . Page load Following that day, a couple of readers added their negative feedback about internal page load time issues. W3 Total Cache wasn’t working as expected and you won’t believe that once the front page load time crossed 25 seconds. (See this report!)

Screenshot_14

 

There could be four reasons:

  • I was using development version of W3 Total Cache
  • Page caching wasn’t sufficient for this high traffic site
  • My theme had too many scripts to load, and
  • There was no lazy-load plugin.

I decided to deactivate the W3 Total Cache plugin and switched to the premium caching tool : WP Rocket.  WP  Rocket is a great and very affordable WordPress caching and speed optimization plugin by a visionary developer team from France.

wp rocket homepage

About

WP Rocket is a caching and website performance improvement plugin for WordPress hosted sites. It works in almost the same way other plugins do : ‘Download’ the plugin files, upload to your WordPress installation’s plugin directly and activate it. The configuration was found to be the easiest of all other plugins available and it took just four or five minutes for me to properly configure it for gauravtiwari.org.

Insights

Features

  • Simple interface. Not too many options. Easy to set-up. No coding required.
  • Image lazyloading at its best. Works with any theme you use and highly reduces the number of HTTP requests for heavy sites.
  • Files Optimization: When activated all CSS, Javascript and HTML files are minified automatically. You can tell plugin to ignore some of the scripts you don’t want to be minimized or concatenated.
  • Mobile Caching : Enables caching for high-end smartphones. Stores website’s static files for better and faster reloading of the pages.
  • Enterprise class Cache preloading.
  • Image Optimization
  • CDN Support
  • Multilingual and multisite support
  • DNS Prefetching

More details about the features are available as a comparison table at WP Rocket Features page.

 

Experience

From the user interface to DNS prefetching, this tool was really a magic. But I was delighted to see the cache preload feature which I couldn’t use on cloudflare as I was a basic subscriber. Cache pre-loading could have cost me $240 per year on Cloudflare but WPRocket did the same at a nominal price. Cache pre-loading boosted the site speed by up to 400%.  I was blown away after the results:

Screenshot_17

It is said, first impression is the last impression” and WP Rocket really made the one on me. I have been using WP Rocket for last two months and my site has suffered no issues at all. Now I am using DIVI 2.0 WordPress theme from Elegant Themes, which is both feature and script heavy. But thanks to WP Rocket, blog articles load as quick they should, codes are not broken and theme design is not compromised by even a single pixel — what else do I need? Top notch plugin, for sure.

Should I buy it?

WP Rocket is suggested to all WordPress bloggers, who can spend a few bucks for the sake of speed and optimization. It is highly recommended for heavy sites with average/slow web hosts. WP Rocket is priced at USD 39 for one and USD 99 for three WordPress installations . It can be purchased from WP Rocket’s Pricing page.

PS: While buying you may see a few French phrases on their site on time by time. Tiny human mistakes and probably this is how multilingual sites (mis)behave.

Support

WP Rocket plugin itself has great video tutorials on TUTORIALS tab inside the plugin configuration page. Frequently Asked Questions (FAQs) are answered in another tab FAQ. If you are seeking for further custom support, you can use WP Rocket Support Forum.

 

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